Download - DYNAMICS OF MACHINERY: Kinetostatic Analysis of the Stephenson III Six-Bar Linkage With a Spring and a Damper

NATIONAL CHENG KUNG UNIVERSITY

Department of Mechanical Engineering

DYNAMICS OF MACHINERY

HOMEWORK 2

Professor name: Chiou, Shen-Tarng

Student name: Nguyen Van Thanh

Student ID: P96007019

Class: N1-047 Dynamics of Machinery

Time: [3] 5 7

1

Content

The Problem No.2 2

Introduction 4

The solution 5

1.The Newtonian solution method and the explanation of the word ‘Kinetostatics’ 5

2.Solving 7

2.1.The first case – all are considered 8

2.1.1.Bearing forces on each joint, and driving torque. 14

2.1.2.Peak, rms/mean value and fluctuation of each bearing force and driving torque 14

2.1.3.The joint force indexes 15

2.2.The second – only the inertial effects are considered 16




2.3.The third – only the gravity forces are neglected 16




2.4.The fourth – only the inertial effects are neglected 17




Result & discussion 18

Conclusions & suggestions 20

References 21

Appendix 22

2

The Problem No.2

Dynamics of Machinery

Kinetostatic Analysis of the Stephenson III Six-bar Linkage with a Spring and a

Damper

Homework #2 (16%) Due to 04/13/2011

Please develop programs on a PC and using the package for the kinetostatic analysis of the

Stephenson III Six-bar Linkage, when the operating speeds are 10, 30, 60, 90, and 120

rad/sec, respectively. The free-body diagrams are shown in Fig. 1. The process torque

acting on link 6, T6 = -12(6 – 289o) Nm, if 6 0 and 6 289

o; otherwise T6 = 0.

Please consider the following situations respectively, (a) only the inertial effects are

considered; (b) only the gravity forces are neglected; (c) only the inertial effects are

neglected; (d) all are considered. In each situation, the required results should at least

include:

(i) Bearing force (Cartesian components, resultant, and direction) on each joint, and

driving torque (should be checked with the energy method);

(ii) peak, and rms values, and fluctuation of each bearing force, and the peak, mean,

and fluctuation of the driving torque. (You may investigate the relations between

these amounts with respect to the operating speed);

(iii) the joint force indexes.

Please (1) based on the results of situation (a) above, investigate the relations between the

peak input torque and the input speed; (2) based on the results of (b) & (d), estimate the

errors by neglecting the gravity forces with each operating speed; (3) based on the results

of (c) & (d), estimate the errors by neglecting the inertial effects with each operating

speed.

項目配分得分

結果與討論 40%

結論與建議 10%

報告寫作 40%

報告美觀 10%

總得分 100%

3

22r

2

2l

3r

3

3r

33l

34

4

4r

4l

5r5

55

5r

5l

6r

6

6

6l

2m g

3m g

4m g

6m g

5m g

12F

32F

32F

53F

43F

43F

14F

65F

16F

dF

sF

53F

65F

T

6T

Fig. 1 Free-body diagrams of moving links

Table 1 Dimensions of the mechanism

i r

i

(mm)

ri

(mm)

mi (kg)

li (mm)

i

(deg)

I i (kg-m2

)

i

(deg) i

(deg)

1 87.01 15.01 --- --- --- --- 0.00 ---

2 30.43 --- 37.49 25.12 0.00 0.0307 --- ---

3 78.61 51.62 62.78 38.81 12.32 1.0941 --- 30.75

4 55.92 --- 50.89 40.33 -8.78 0.6700 --- ---

5 88.45 44.91 21.19 37.71 10.25 0.4420 --- 30.82

6 98.91 --- 32.90 52.62 5.42 1.1271 --- ---

7 130.03 45.01 --- --- --- --- 0.00 ---

4

Introduction

The main objective of this report is to provide students with the opportunity to learn and

improve their programming skills using the Matlab environment to solve the problem in

Kinematic & Kinetostatics analysis (the word ‘Kinetostatics’ was briefly explained in the

contend). In these report, we assume that the Kinematic analysis was completed. That

means we already know the state of motion (position, velocity and acceleration) of every

linkage and particular points of interest (mass centers). With this basic Matlab in

Kinetostatic analysis problem solving, the report provides opportunities to explore the

application of Matlab in Mechanical Engineering. The problem we want to solve is

Kinetostatic analysis of the Stephenson III six-bar linkage with a Spring and a

Damper.The report is a practice for everyone to learn about Kinematic & Kinetostatic

Analysis, programming, and the application of Matlab in Mechanical Engineering. So,

there are have a lot of commercial softwares also can do the problem for more convenient,

but maybe I can do use it in further reports. Now, I would like to use Matlab to solve this

problem.

5

The solution

1. The Newtonian solution method and the explanation of the word

‘Kinetostatics’

In the previous homework (HW1), we have has dealt with the kinematics of

mechanism while temporarily ignoring the forces and torque present in those

mechanisms. This homework will address the problem of determining the forces

present and torque in moving mechanisms and machinery. This problem is called

dynamic force analysis. We use the Newtonian solution method to solve the problem.

Dynamic force analysis can be done by any of several methods. The one which gives

the most information about forces internal to the mechanism requires only the use of

the Newton’s laws as defined in the following equations:

For a body in plane motion:

∑

∑

Where m = mass of the body.

= acceleration of the center of

mass.

= a typical external force.

∑ = summation of all external

forces.

∑ = summation of moments of all external forces, around axis through

the center of mass perpendicular to the plane of motion.

I = moment of inertia of the body around the axis through the center of

mass and perpendicular to the plane of motion.

= angular acceleration of the body.

We can differentiate between two subclasses of dynamics problem depending upon

which quantities are known and which are to be found. The ‘forward dynamics

problem’ is the one in which we know everything about the external loads (forces

and/or torques) being exerted on the system, and we wish to determine the

accelerations, velocities and displacements which result from the application of those

forces and torques this means given forces and/or torques and m/I, solve for and/or

, for example. The second subclass of dynamics problem, called the ‘inverse

dynamics problem’ is one in which we know the (desired) accelerations, velocities,

and displacements to be imposed upon our system and wish to solve for the

6

magnitudes and direction of the forces and torques which are necessary to provide the

desired motions and which result from them. This inverse dynamics case is sometimes

also called Kinetostatics. Given and/or and m/I solve for forces and/or torques.

In this homework, we do the Kinetostatics analysis.

It is convenient to separately sum force components

in X and Y directions, with the coordinate system

chosen for convenience. The moments in our two

dimensional system are all in the Z direction. This let

us break the forces equations in two scalar equations:

Fex = m*Agx

Fey = m*Agy.

Mg = [(re/g * cos e)* Fey – (re/g * sin e)* Fex]

Where,

Fex, Fey = X, Y components of vector Fe.

Agx, Agy = X, Y components of vector Ag.

e = direction of vector Fe

re/g = the distance from the center of mass (G) to the point that external force

locate.

A complete force analysis for a mechanism would consist of writing the three scalar

equations above for each moving part (link) of the mechanism, the solving the

resulting set of equations for the unknowns. We repeat again that the problem in this

report is do the Kinetostatics analysis that means determining all the reaction forces

between links and driving torque.

7

2. Solving

Before calculating bearing forces and torque, We have to know the the force of Spring

act on the link 3. This force is calculated by equation:

Fs = K*(rs – rs0)

Where K is the stiffness ( 20 N mmK ).

rs0 is the initial length of the Spring (rs0 = 91.52 mm).

rs is the length of the Spring at s. The value of rs is given by the Kinematics

analysis in the previous report.

And the force of Damper act on the link 5 is calculated by equation:

Where dc is the damping coefficient, (dc = 220 N.s/mm).

fd is the kinematic coefficient, mm. The value of fd is given by the Kinematics

analysis in the previous report.

I would like to choose the first case is situation (d) – all are considered and I will do

the first case first

8

2.1. The first case – all are considered

The first step is making the free-body sketches of the moving links:

22r

2

2l

3r

3

3r

33l

34

4

4r

4l

5r5

55

5r

5l

6r

6

6

6l

2m g

3m g

4m g

6m g

5m g

12F

32F

32F

53F

43F

43F

14F

65F

16F

dF

sF

53F

65F

T

6T

Fig. 1 Free-body diagrams of moving links

9

Next step, we have to write the force equations for each link.

Link 2:

F12x + F32x = m2*Ag2x (1)

F12y + F32y + m2*g = m2*Ag2y (2)

Link 3:

-F32x + F43x + F53x + Fsx = m3*Ag3x (3)

-F32y + F43y + F53y + Fsy + m3*g = m3*Ag3y (4)

Link 4:

-F43x + F14x = m4*Ag4x (5)

-F43y + F14y + m4*g = m4*Ag4y (6)

10

Link 5:

-F53x + F65x + Fdx = m5*Ag5x (7)

-F53y + F65y + Fdy + m5*g = m5*Ag5y (8)

Link 6:

-F65x + F16x = m6*Ag6x (9)

-F65y + F16y + m6*g = m6*Ag6y (10)

Write the moment equations for each link:

Link 3: take the moments around the axis through point A and perpendicular to the

plane of motion.

T + (r2*cos 2*F32y - r2*sin 2*F32x) + l2*cos (2 + 2)*m2*g = (l2*cos (2 +

2)*m2*Ag2y - l2*sin (2 + 2)*m2*Ag2x) + I2*2 (11)

A

11

Link 3: take the moments around the axis through point B and perpendicular to the

plane of motion.

(r3*cos 3*F43y – r3*sin 3*F43x) + (r’3*cos (3 + 3’)*(F53y + Fsy) – r’3* sin (3 +

3’)*(F53x + Fsx)) + l3*cos (3 + 3)*m3*g = (l3*cos (3 + 3)*m3*Ag3y – l3*sin (3 +

3)*m3*Ag3x) + I3*3 (12)

Link 4: take the moments around the axis through point C and perpendicular to the

plane of motion.

(r4*cos 4*F14y – r4*sin 4*F14x) + l4*cos (4 + 4)*m4*g = (l4*cos (4 + 4)*m4*Ag4y –

l4*sin (4 + 4)*m4*Ag4x) + I4*4 (13)

B

C

12

Link 5: take the moments around the axis through point E and perpendicular to the

plane of motion.

(r5*cos 5*F65y – r5*sin 5*F65x) + (r’5*cos (5 + 5’)*Fdy – r’5* sin (5 + 5)*Fdx) +

l5*cos (5 + 5’)*m5*g = (l5*cos (5 + 5)*m5*Ag5y – l5*sin (5 + 5)*m5*Ag5x) + I5*5

(14)

Link 5: take the moments around the axis through point F and perpendicular to the

plane of motion.

T6 + (r6*cos 6*F16y – r6*sin 6*F16x) + l6*cos (6 + 6)*m6*g = (l6*cos (6 +

6)*m6*Ag6y – l6*sin (6 + 6)*m6*Ag6x) + I6*6 (15)

E

F

13

So there are fifteen linear equations through (1) to (15), and fifteen unknown variables

(F12x, F12y, F14x, F14y, F16x, F16y, F32x, F32y, F43x, F43y, F53x, F53y, F65x, F65y, and T). And

we can express the fifteen equations in matrix form:

A * F = B

Where F is the vector (column matrix) of fifteen unknowns,

B is the vector (column matrix) of fifteen quantities,

A is the 15 x 15 matrix of coefficients of the unknowns.

F = [F12x; F12y; F14x; F14y; F16x; F16y; F32x; F32y; F43x; F43y; F53x; F53y; F65x; F65y; T].

B = [b1; b2; b3; b4; b5; b6; b7; b8; b9; b10; b11; b12; b13; b14; b15].

Where,

b1=m2*Ag2x

b2 =m2* Ag2y - m2*g;

b3 =m3* Ag3x - Fsx;

b4 =m3* Ag3y - m3*g - Fsy;

b5 =m4* Ag4x;

b6 =m4* Ag4y - m4*g;

b7 =m5* Ag5x - Fdx;

b8 =m5* Ag5y - m5*g - Fdy;

b9 =m6* Ag6x;

b10 =m6* Ag6y - m6*g;

b11 = (l2*cos (2 + 2)*m2*Ag2y - l2*sin (2 + 2)*m2*Ag2x) + I2*2 - l2*cos (2 +

2)*m2*g;

b12 = (l3*cos (3 + 3)*m3*Ag3y – l3*sin (3 + 3)*m3*Ag3x) + I3*3 - (r’3*cos (3 +

3’)*Fsy – r’3* sin (3 + 3’)*Fsx) - l3*cos (3 + 3)*m3*g

b13 = (l4*cos (4 + 4)*m4*Ag4y – l4*sin (4 + 4)*m4*Ag4x) + I4*5 - l4*cos (4 +

4)*m4*g;

b14 = (l5*cos (5 + 5)*m5*Ag5y – l5*sin (5 + 5)*m5*Ag5x) + I5*5 - (r’5*cos (5 +

5’)*Fdy – r’5* sin (5 + 5’)*Fdx) - l5*cos (5 + 5)*m5*g;

b15 = (l6*cos (6 + 6)*m6*Ag6y – l6*sin (6 + 6)*m6*Ag6x) + I6*6 - l6*cos (6 +

6)*m6*g – T6;

14

A = [a1; a2; a3; a4; a5; a6; a7; a8; a9; a10; a11; a12; a13; a14; a15].

Where,

a1 = [1 0 0 0 0 0 1 0 0 0 0 0 0 0 0];

a2 = [0 1 0 0 0 0 0 1 0 0 0 0 0 0 0];

a3 = [0 0 0 0 0 0 -1 0 1 0 1 0 0 0 0];

a4 = [0 0 0 0 0 0 0 -1 0 1 0 1 0 0 0];

a5 = [0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0];

a6 = [0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0];

a7 = [0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0];

a8 = [0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0];

a9 = [0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0];

a10 = [0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0];

a11 = [0 0 0 0 0 0 -r2*sin2 r2*cos2 0 0 0 0 0 0 1];

a12 = [0 0 0 0 0 0 0 0 -r3*sin3 r3*cos3 -r3'*sin (3+ 3’) r3’*cos (3+ 3’) 0 0 0];

a13 = [0 0 -r4*sin4 r4*cos4 0 0 0 0 0 0 0 0 0 0 0];

a14 = [0 0 0 0 0 0 0 0 0 0 0 0 -r5*sin5 r5*cos5 0]

a15 = [0 0 0 0 –r6*sin6 r6*cos6 0 0 0 0 0 0 0 0 0];

Hence, F = inv (A)* B.

2.1.1. Bearing forces on each joint, and driving torque.

With omage 2 = 10 rad/s please refer to the Appendix A4, B4, B24

30 …………………………………... A8, B8, B28

60 ……………………………………A12, B12, B32

90 ……………………………………A16, B16, B36

120 ………………………………….. A20, B20, B40

2.1.2. Peak, rms/mean value and fluctuation of each bearing force and driving torque

Please refer to the Appendix A21, and

With omage 2 = 10 rad/s please refer to the Appendix B4, B24

30 …………………………………... B8, B28

60 …………………………………… B12, B32

90 …………………………………… B16, B36

120 ………………………………….. B20, B40

15

2.1.3. The joint force indexes

Holte and Chase define a joint-force index (JFI) which is useful as an indicator of

any linkage’s ability to smoothly transmit energy regardless of where the loads are

applied on the linkage. The JFI at any instantaneous position is defined as the ratio

of the maximum static force in any joint of the mechanism to the applied external

load. If the external load is a force, then it is:

JFI = Max (abs ((Fij)/Fext))) for all pairs i, j

If the external load is a torque, then it is:

JFI = Max (abs ((Fij)/Text))) for all pairs i, j

Where, in both cases, Fij is the force in the linkage joint connecting links i and j.

The Fij are calculated from a static force analysis of the linkage. Dynamic force can

be much greater than static forces if speeds are high. However, if this static force

transmission index indicates a problem in the absence of any dynamic forces, then

the situation will obviously be worse at speed. The largest joint force at each

position is used rather than a composite or average value on the assumption that

high friction in any one joint is sufficient to hamper linkage performance regardless

of the forces at other joints.

In this report, the external load is the torque (T6), right? If so the joint-force index

is,

JFI = Max (abs ((Fij)/T6))) for all pairs i, j

Fij can be F12, F14, F16, F32, F43, F53, and F65 at each position of the mechanism. As

we know, the Fij are calculated from a static force analysis of the linkage that means

the masses and inertias are neglected. Note that we have the process torque acting

on link 6, T6 = -12(6 – 289o) Nm, if 6 0 and 6 289

o; otherwise T6 = 0. So T6

can become zero at some position of the mechanism and then the JFI will become

infinite. That means the linkage reachs an immovalbe postion, defined as the input

link or input joint being inactive. These position need to be identified and avoided

in any event, independent of the determination of any index of merit. In some cases

the mechanism may be immovable but still capable of supporting a load.

16

2.2. The second – only the inertial effects are considered

Now we substitute the mass (m) of each link = 0 and the gravity force (g) = 0 in the

first case, so we immediately obtain the result.


With omage2 = 10 rad/s please refer to the Appendix A1, B1, B21

30 …………………………………... A5, B5, B25

60 ……………………………………A9, B9, B29

90 ……………………………………A13, B13, B33

120 ………………………………….. A17, B17, B37



With omage2 = 10 rad/s please refer to the Appendix B1, B21

30 …………………………………... B5, B25

60 ……………………………………B9, B29

90 ……………………………………B13, B33

120 ………………………………….. B17, B37


2.3. The third – only the gravity forces are neglected

Now we substitute the gravity force (g) = 0 in the first case, so we immediately

obtain the result.



30 …………………………………... A5, B5, B25

60 ……………………………………A9, B9, B29

90 ……………………………………A13, B13, B33

120 ………………………………….. A17, B17, B37




30 …………………………………... B5, B25

60 ……………………………………B9, B29

90 ……………………………………B13, B33

120 ………………………………….. B17, B37

17


2.4. The fourth – only the inertial effects are neglected

Now we substitute the moment of inertia = 0 in the first case, so we immediately

obtain the result.



30 …………………………………... A7, B7, B27

60 ……………………………………A11, B11, B31

90 ……………………………………A15, B15, B35

120 ………………………………….. A19, B19, B39




30 …………………………………...B7, B27

60 ……………………………………B11, B31

90 ……………………………………B15, B35

120 ………………………………….. B19, B39


18

Result & discussion

1. We can see that the peak values of bearing forces on each joint and driving torque

increase if the input speed increase for situation (b), (c) and (d) except the situation

(a), the peak values seem to be unvaried.

1

19

2. The errors by neglecting the gravity forces and the errors by neglecting the inertial

effects seem to be unvaried when the input speed vary.

3. The effect by neglecting the inertias is more than by neglecting the gravity forces.

20

Conclusions & suggestions

After reading the report, you can understand the Kinetostatic Analysis of the

Stephenson III Six-bar Linkage and every mechanism as well. And you also

understand the effect of inertia, gravity force and mass on solving the problem. In

this report, the frictions are neglected, so you can add the frictions and solving the

problem. After calculating, you can estimate the errors by neglecting the frictions.

21

References 1. Allen S. Hall, Jr., 1986, Notes on mechanism analysis, Waveland Press, Prospect

Heights, Illinois, USA.

2. Norton, Robert L., 1999, Design of machinery: an introduction to the synthesis

and analysis of mechanisms and machines, 2nd ed, McGraw-Hill, Boston, New

York, USA.

3. Otto, S. R. (Stephen Robert)/Denier, J. P./Springer, 2005, An introduction to

programming and numerical methods in MATLAB, Springer, London.

4. Rao V. Dukkipati, 2009, MATLAB for mechanical engineers, Tunbridge Wells,

Kent TN1 1YS, UK

5. Roger F. Gans, 1991, Analytical kinematics :analysis and synthesis of planar

mechanisms, Butterworth-Heinemann, USA

22

Appendix

Appendix A1

Bearing forces (Cartesian components, resultant, and direction) on each joint, and driving torqure, when omega = 10, only the inertial effects are considered

theta2

degree

F12x

/10.^4

N

F12y

/10.^4

N

F12

/10.^4

N

theta12

degree

F14x

/10.^4

N

F14y

/10.^4

N

F14

/10.^4

N

theta14

degree

F16x

/10.^4

N

F16y

/10.^4

N

F16

/10.^4

N

theta16

degree

0 5.5462 23.1636 23.8183 76.5348 2.2316 -6.7533 7.1125 288.2861 3.2081 -5.4226 6.3006 300.6093

5 3.9752 14.7676 15.2932 74.9339 1.1215 -4.1187 4.2687 285.2324 1.867 -3.684 4.13 296.8755

10 3.2229 10.6665 11.1428 73.1877 0.6275 -2.8396 2.9081 282.4614 1.1857 -2.7899 3.0314 293.0251

15 2.6075 7.8758 8.2962 71.6815 0.3442 -1.9399 1.9702 280.0613 1.0286 -1.9548 2.2089 297.7537

20 2.3741 6.5685 6.9844 70.128 0.2108 -1.4905 1.5053 278.0514 0.817 -1.6753 1.8639 295.9966

25 2.2918 5.8723 6.3037 68.6812 0.1375 -1.2102 1.218 276.4795 0.6972 -1.535 1.6859 294.4291

30 2.3297 5.5834 6.0499 67.3514 0.0969 -1.032 1.0365 275.3638 0.6344 -1.4897 1.6192 293.0685

35 2.4645 5.5724 6.0931 66.1414 0.0753 -0.9141 0.9172 274.7085 0.6079 -1.51 1.6278 291.9308

40 2.9212 6.1813 6.8368 64.7052 0.0734 -0.9433 0.9462 274.4462 0.3507 -1.8921 1.9244 280.5007

45 3.1917 6.4654 7.2103 63.7264 0.0711 -0.8699 0.8728 274.6709 0.358 -1.9742 2.0064 280.2789

50 3.4963 6.8194 7.6635 62.8558 0.0747 -0.8061 0.8095 275.2933 0.376 -2.0658 2.0998 280.3165

55 3.8171 7.2041 8.1529 62.0828 0.0821 -0.747 0.7515 276.2712 0.4015 -2.1559 2.193 280.5484

60 4.1383 7.5894 8.6443 61.3978 0.0916 -0.6904 0.6964 277.5587 0.4322 -2.2366 2.278 280.9368

65 4.446 7.9529 9.1113 60.793 0.1019 -0.6352 0.6433 279.1097 0.4668 -2.3027 2.3495 281.4598

70 4.7292 8.2782 9.5338 60.2612 0.1117 -0.5812 0.5919 280.8807 0.5043 -2.3514 2.4049 282.1035

75 4.979 8.5536 9.8972 59.7967 0.1203 -0.5283 0.5418 282.8328 0.5437 -2.382 2.4432 282.8576

80 5.1419 8.5813 10.0039 59.07 0.0941 -0.3604 0.3725 284.6345 0.5814 -2.4031 2.4725 283.6005

85 5.3126 8.7235 10.2139 58.6585 0.0886 -0.2912 0.3044 286.9172 0.6246 -2.4063 2.486 284.5504

90 5.4397 8.8075 10.3519 58.2997 0.0792 -0.2255 0.239 289.35 0.668 -2.3948 2.4862 285.5861

95 5.5207 8.832 10.4155 57.9914 0.0662 -0.1643 0.1772 291.9281 0.7108 -2.3698 2.4741 286.696

100 5.5541 8.7967 10.4033 57.7325 0.0497 -0.1083 0.1192 294.6748 0.7519 -2.3325 2.4507 287.8679

105 5.5387 8.7014 10.3146 57.5219 0.0305 -0.058 0.0655 297.74 0.7903 -2.2838 2.4167 289.0885

110 5.4739 8.546 10.1488 57.3597 0.0091 -0.0139 0.0166 303.1101 0.8247 -2.2244 2.3724 290.3428

115 5.3908 8.3355 9.9268 57.108 0.0068 -0.0095 0.0117 305.4673 0.8184 -2.11 2.2631 291.1988

120 5.2277 8.0552 9.6029 57.0168 -0.0101 0.0153 0.0183 123.5686 0.8315 -2.0213 2.1856 292.3617

125 5.0114 7.7087 9.1944 56.9721 -0.0249 0.0325 0.041 127.5236 0.8339 -1.9208 2.094 293.4673

130 4.7384 7.2896 8.6943 56.9756 -0.0364 0.0423 0.0558 130.7408 0.8226 -1.8074 1.9858 294.4703

135 4.4024 6.7867 8.0895 57.029 -0.0432 0.0449 0.0623 133.9051 0.7936 -1.6788 1.8569 295.2998

140 3.9922 6.1791 7.3566 57.1341 -0.0439 0.0407 0.0599 137.1773 0.741 -1.5307 1.7006 295.8299

145 3.4863 5.4287 6.4517 57.2917 -0.0372 0.0304 0.0481 140.7707 0.655 -1.3552 1.5052 295.7968

150 2.8413 4.4596 5.2878 57.4982 -0.0215 0.0148 0.0261 145.4581 0.5181 -1.1367 1.2492 294.5029

155 1.9606 3.1057 3.6728 57.7364 0.006 -0.0049 0.0078 321.0997 0.2931 -0.8412 0.8908 289.2081

160 0.5854 0.9315 1.1002 57.8521 0.0549 -0.0268 0.0611 333.9643 -0.1152 -0.3789 0.396 253.0878

165 -3.0203 -4.9907 5.8334 238.8185 0.1601 -0.0112 0.1605 356.0133 -1.3083 0.8394 1.5545 147.3164

170 -20.9374 -32.4353 38.606 237.1573 2.0761 0.259 2.0922 7.1097 -6.6976 6.7178 9.4861 134.9135

175 18.8367 38.9358 43.253 64.1829 3.5344 -0.2824 3.5456 355.4315 8.3595 -7.8085 11.4391 316.9522

180 9.0381 17.6225 19.8051 62.8479 0.9724 -0.2262 0.9984 346.907 3.6993 -3.6673 5.209 315.2488

185 6.3773 12.6836 14.1966 63.3068 0.7264 -0.2209 0.7592 343.088 2.6916 -2.6582 3.783 315.3569

190 5.0437 10.3864 11.5462 64.0984 0.6896 -0.2316 0.7275 341.4376 2.22 -2.1955 3.1223 315.3179

195 4.1638 8.9551 9.8757 65.0633 0.7055 -0.2457 0.7471 340.7983 1.9309 -1.9048 2.7123 315.3904

200 3.5042 7.9236 8.6639 66.1427 0.7385 -0.2602 0.783 340.588 1.7226 -1.6946 2.4164 315.4704

205 2.9737 7.1096 7.7064 67.3025 0.7744 -0.2737 0.8214 340.5352 1.5559 -1.5292 2.1815 315.4949

210 2.5294 6.4264 6.9062 68.5159 0.8059 -0.2853 0.8549 340.5075 1.412 -1.3916 1.9825 315.4165

215 2.0206 5.4458 5.8086 69.6432 0.7692 -0.2556 0.8106 341.6179 1.1865 -1.2122 1.6962 314.3876

220 1.7018 4.9191 5.2051 70.9169 0.7804 -0.2602 0.8226 341.5634 1.0657 -1.1096 1.5385 313.844

225 1.4246 4.4328 4.6561 72.1834 0.7786 -0.262 0.8215 341.4039 0.9495 -1.0169 1.3913 313.038

230 1.1827 3.9746 4.1468 73.4288 0.7632 -0.2609 0.8066 341.1287 0.8354 -0.9314 1.2512 311.8917

235 0.971 3.5351 3.6661 74.6415 0.7341 -0.2566 0.7777 340.7333 0.7216 -0.8511 1.1158 310.2926

240 0.7855 3.1068 3.2046 75.8108 0.6913 -0.2487 0.7347 340.2166 0.6064 -0.7743 0.9835 308.0695

245 0.6231 2.6832 2.7546 76.9265 0.6349 -0.2364 0.6775 339.5784 0.4889 -0.6995 0.8534 304.9464

250 0.481 2.2585 2.3092 77.9765 0.5649 -0.2189 0.6058 338.8185 0.3678 -0.6256 0.7257 300.4539

255 0.3571 1.8272 1.8618 78.9427 0.4813 -0.1951 0.5193 337.9357 0.2425 -0.5511 0.6021 293.7491

260 0.2493 1.384 1.4063 79.7885 0.384 -0.1636 0.4174 336.9261 0.1121 -0.4748 0.4879 283.2844

265 0.1705 1.0124 1.0267 80.4406 0.2935 -0.1379 0.3243 334.8413 0.0007 -0.4098 0.4098 270.0931

270 0.0848 0.5024 0.5095 80.4156 0.163 -0.0808 0.1819 333.6453 -0.1484 -0.3222 0.3548 245.2653

275 -0.0519 -0.3951 0.3984 262.5217 -0.1035 0.0535 0.1165 152.6625 -0.1179 0.0683 0.1363 149.897

280 -0.1099 -0.9718 0.978 263.5502 -0.2638 0.1447 0.3009 151.2659 -0.2825 0.1708 0.3302 148.8413

285 -0.1599 -1.5928 1.6009 264.2668 -0.4393 0.2563 0.5086 149.7419 -0.4543 0.2829 0.5352 148.0903

290 -0.2048 -2.2707 2.2799 264.8458 -0.6307 0.3931 0.7432 148.0667 -0.6345 0.4074 0.754 147.2999

295 -0.2482 -3.0216 3.0318 265.3045 -0.8394 0.5613 1.0098 146.2286 -0.8247 0.5477 0.99 146.4131

300 -0.295 -3.8676 3.8789 265.6388 -1.0671 0.7691 1.3154 144.218 -1.0275 0.7086 1.2482 145.4096

305 -0.3521 -4.8394 4.8522 265.8382 -1.3162 1.0273 1.6696 142.0272 -1.2468 0.8966 1.5358 144.2782

310 -0.4299 -5.9814 5.9969 265.889 -1.5902 1.351 2.0866 139.6503 -1.4887 1.1213 1.8637 143.0116

315 -0.5437 -7.3622 7.3823 265.7763 -1.8954 1.7623 2.5881 137.0846 -1.7632 1.3972 2.2497 141.6049

320 -0.7296 -9.1784 9.2073 265.4551 -2.2681 2.3217 3.2457 134.3302 -2.0837 1.7749 2.7371 139.576

325 -1.0052 -11.4487 11.4927 264.9822 -2.676 3.0357 4.0468 131.3965 -2.4914 2.2399 3.3502 138.0431

330 -1.4638 -14.6814 14.7542 264.3061 -3.201 4.0539 5.1654 128.2951 -3.0502 2.9119 4.2169 136.3292

335 -2.6179 -21.7801 21.9369 263.1461 -4.2096 6.2758 7.5569 123.8522 -4.2877 4.3884 6.1353 134.3345

340 -4.7284 -33.9193 34.2473 262.064 -5.9094 9.9447 11.568 120.7201 -6.3534 6.9827 9.4405 132.2982

345 -11.8075 -73.1268 74.074 260.8278 -11.2882 21.5923 24.3649 117.5999 -13.0154 15.4237 20.1814 130.1596

350 79.5354 484.1942 490.6831 80.6717 73.3959 -155.2479 171.7233 295.3032 78.5826 -97.2656 125.0433 308.9354

355 11.2588 55.3298 56.4637 78.4981 6.7313 -16.7572 18.0586 291.8852 8.4471 -12.1309 14.7822 304.8505

360 5.5462 23.1636 23.8183 76.5348 2.2316 -6.7533 7.1125 288.2861 3.2081 -5.4226 6.3006 300.6093

Appendix A1


theta2

degree

F32x

/10.^4

N

F32y

/10.^4

N

F32

/10.^4

N

theta32

degree

F43x

/10.^4

N

F43y

/10.^4

N

F43

/10.^4

N

theta43

degree

F53x

/10.^4

N

F53y

/10.^4

N

F53

/10.^4

N

theta53

degree

F65x

/10.^4

N

F65y

/10.^4

N

F65

/10.^4

N

theta65

degree

T/10.^3

N.m

0 -5.5462 -23.164 23.818 256.535 2.2316 -6.7533 7.1125 288.286 -7.7863 -16.4171 18.17 244.626 3.2081 -5.4226 6.3006 300.609 70487

5 -3.9752 -14.768 15.293 254.934 1.1215 -4.1187 4.2687 285.232 -5.1025 -10.6534 11.8123 244.408 1.867 -3.684 4.13 296.876 43712

10 -3.2229 -10.667 11.143 253.188 0.6275 -2.8396 2.9081 282.461 -3.8551 -7.8307 8.7282 243.789 1.1857 -2.7899 3.0314 293.025 30262

15 -2.6075 -7.8758 8.2962 251.682 0.3442 -1.9399 1.9702 280.061 -2.9558 -5.9393 6.6341 243.542 1.0286 -1.9548 2.2089 297.754 21096

20 -2.3741 -6.5685 6.9844 250.128 0.2108 -1.4905 1.5053 278.051 -2.5887 -5.081 5.7025 243.001 0.817 -1.6753 1.8639 295.997 16312

25 -2.2918 -5.8723 6.3037 248.681 0.1375 -1.2102 1.218 276.48 -2.4327 -4.665 5.2612 242.458 0.6972 -1.535 1.6859 294.429 13248

30 -2.3297 -5.5834 6.0499 247.351 0.0969 -1.032 1.0365 275.364 -2.4299 -4.5541 5.1618 241.917 0.6344 -1.4897 1.6192 293.069 11169

35 -2.4645 -5.5724 6.0931 246.141 0.0753 -0.9141 0.9172 274.709 -2.543 -4.6609 5.3095 241.383 0.6079 -1.51 1.6278 291.931 9588.6

40 -2.9212 -6.1813 6.8368 244.705 0.0734 -0.9433 0.9462 274.446 -2.9975 -5.2404 6.0371 240.23 0.3507 -1.8921 1.9244 280.501 8695.2

45 -3.1917 -6.4654 7.2103 243.726 0.0711 -0.8699 0.8728 274.671 -3.2655 -5.5977 6.4806 239.742 0.358 -1.9742 2.0064 280.279 7044.1

50 -3.4963 -6.8194 7.6635 242.856 0.0747 -0.8061 0.8095 275.293 -3.5735 -6.0154 6.9968 239.287 0.376 -2.0658 2.0998 280.317 5188.6

55 -3.8171 -7.2041 8.1529 242.083 0.0821 -0.747 0.7515 276.271 -3.9016 -6.459 7.5459 238.866 0.4015 -2.1559 2.193 280.548 3059.1

60 -4.1383 -7.5894 8.6443 241.398 0.0916 -0.6904 0.6964 277.559 -4.232 -6.9008 8.0951 238.481 0.4322 -2.2366 2.278 280.937 641.693

65 -4.446 -7.9529 9.1113 240.793 0.1019 -0.6352 0.6433 279.11 -4.5499 -7.3193 8.6182 238.134 0.4668 -2.3027 2.3495 281.46 -2034

70 -4.7292 -8.2782 9.5338 240.261 0.1117 -0.5812 0.5919 280.881 -4.8427 -7.6984 9.0949 237.828 0.5043 -2.3514 2.4049 282.104 -4907.5

75 -4.979 -8.5536 9.8972 239.797 0.1203 -0.5283 0.5418 282.833 -5.1009 -8.0266 9.5103 237.564 0.5437 -2.382 2.4432 282.858 -7898

80 -5.1419 -8.5813 10.004 239.07 0.0941 -0.3604 0.3725 284.635 -5.2375 -8.222 9.7485 237.503 0.5814 -2.4031 2.4725 283.601 -10875

85 -5.3126 -8.7235 10.214 238.659 0.0886 -0.2912 0.3044 286.917 -5.4025 -8.4334 10.0154 237.356 0.6246 -2.4063 2.486 284.55 -13791

90 -5.4397 -8.8075 10.352 238.3 0.0792 -0.2255 0.239 289.35 -5.52 -8.5828 10.2047 237.253 0.668 -2.3948 2.4862 285.586 -16553

95 -5.5207 -8.832 10.416 237.991 0.0662 -0.1643 0.1772 291.928 -5.5878 -8.6685 10.3134 237.194 0.7108 -2.3698 2.4741 286.696 -19078

100 -5.5541 -8.7967 10.403 237.733 0.0497 -0.1083 0.1192 294.675 -5.6046 -8.6891 10.3398 237.177 0.7519 -2.3325 2.4507 287.868 -21293

105 -5.5387 -8.7014 10.315 237.522 0.0305 -0.058 0.0655 297.74 -5.5699 -8.644 10.2831 237.204 0.7903 -2.2838 2.4167 289.089 -23133

110 -5.4739 -8.546 10.149 237.36 0.0091 -0.0139 0.0166 303.11 -5.4834 -8.5325 10.1426 237.273 0.8247 -2.2244 2.3724 290.343 -24547

115 -5.3908 -8.3355 9.9268 237.108 0.0068 -0.0095 0.0117 305.467 -5.3979 -8.3262 9.9229 237.045 0.8184 -2.11 2.2631 291.199 -25587

120 -5.2277 -8.0552 9.6029 237.017 -0.0101 0.0153 0.0183 123.569 -5.2177 -8.0705 9.6103 237.117 0.8315 -2.0213 2.1856 292.362 -26033

125 -5.0114 -7.7087 9.1944 236.972 -0.0249 0.0325 0.041 127.524 -4.9864 -7.7411 9.2081 237.213 0.8339 -1.9208 2.094 293.467 -25946

130 -4.7384 -7.2896 8.6943 236.976 -0.0364 0.0423 0.0558 130.741 -4.7017 -7.3317 8.7097 237.329 0.8226 -1.8074 1.9858 294.47 -25304

135 -4.4024 -6.7867 8.0895 237.029 -0.0432 0.0449 0.0623 133.905 -4.3587 -6.8311 8.1032 237.459 0.7936 -1.6788 1.8569 295.3 -24076

140 -3.9922 -6.1791 7.3566 237.134 -0.0439 0.0407 0.0599 137.177 -3.9475 -6.2192 7.3662 237.595 0.741 -1.5307 1.7006 295.83 -22213

145 -3.4863 -5.4287 6.4517 237.292 -0.0372 0.0304 0.0481 140.771 -3.4481 -5.4583 6.4562 237.719 0.655 -1.3552 1.5052 295.797 -19617

150 -2.8413 -4.4596 5.2878 237.498 -0.0215 0.0148 0.0261 145.458 -2.8188 -4.4736 5.2876 237.785 0.5181 -1.1367 1.2492 294.503 -16075

155 -1.9606 -3.1057 3.6728 237.736 0.006 -0.0049 0.0078 321.1 -1.9665 -3.1007 3.6717 237.617 0.2931 -0.8412 0.8908 289.208 -11087

160 -0.5854 -0.9315 1.1002 237.852 0.0549 -0.0268 0.0611 333.964 -0.6441 -0.9078 1.1131 234.642 -0.1152 -0.3789 0.396 253.088 -3273

165 3.0203 4.9907 5.8334 58.8185 0.1601 -0.0112 0.1605 356.013 2.8282 4.9759 5.7235 60.3873 -1.3083 0.8394 1.5545 147.316 17048

170 20.9374 32.4353 38.606 57.1573 2.0761 0.259 2.0922 7.1097 18.3316 31.747 36.6595 59.9966 -6.6976 6.7178 9.4861 134.914 108260

175 -18.837 -38.936 43.253 244.183 3.5344 -0.2824 3.5456 355.432 -22.9744 -39.1424 45.3867 239.59 8.3595 -7.8085 11.4391 316.952 -123030

180 -9.0381 -17.623 19.805 242.848 0.9724 -0.2262 0.9984 346.907 -10.1115 -17.4781 20.1923 239.95 3.6993 -3.6673 5.209 315.249 -53625

185 -6.3773 -12.684 14.197 243.307 0.7264 -0.2209 0.7592 343.088 -7.1522 -12.502 14.4032 240.227 2.6916 -2.6582 3.783 315.357 -36758

190 -5.0437 -10.386 11.546 244.098 0.6896 -0.2316 0.7275 341.438 -5.7645 -10.18 11.6989 240.479 2.22 -2.1955 3.1223 315.318 -28460

195 -4.1638 -8.9551 9.8757 245.063 0.7055 -0.2457 0.7471 340.798 -4.8922 -8.7279 10.0055 240.728 1.9309 -1.9048 2.7123 315.39 -23042

200 -3.5042 -7.9236 8.6639 246.143 0.7385 -0.2602 0.783 340.588 -4.2606 -7.6778 8.7808 240.973 1.7226 -1.6946 2.4164 315.47 -19010

205 -2.9737 -7.1096 7.7064 247.303 0.7744 -0.2737 0.8214 340.535 -3.7626 -6.8476 7.8133 241.213 1.5559 -1.5292 2.1815 315.495 -15783

210 -2.5294 -6.4264 6.9062 248.516 0.8059 -0.2853 0.8549 340.508 -3.3471 -6.1507 7.0025 241.446 1.412 -1.3916 1.9825 315.417 -13087

215 -2.0206 -5.4458 5.8086 249.643 0.7692 -0.2556 0.8106 341.618 -2.7989 -5.1975 5.9032 241.698 1.1865 -1.2122 1.6962 314.388 -10048

220 -1.7018 -4.9191 5.2051 250.917 0.7804 -0.2602 0.8226 341.563 -2.4896 -4.665 5.2877 241.912 1.0657 -1.1096 1.5385 313.844 -8138.1

225 -1.4246 -4.4328 4.6561 252.183 0.7786 -0.262 0.8215 341.404 -2.2093 -4.1758 4.7242 242.118 0.9495 -1.0169 1.3913 313.038 -6472.7

230 -1.1827 -3.9746 4.1468 253.429 0.7632 -0.2609 0.8066 341.129 -1.9509 -3.7177 4.1985 242.312 0.8354 -0.9314 1.2512 311.892 -5017.3

235 -0.971 -3.5351 3.6661 254.642 0.7341 -0.2566 0.7777 340.733 -1.7091 -3.2817 3.7001 242.49 0.7216 -0.8511 1.1158 310.293 -3749.8

240 -0.7855 -3.1068 3.2046 255.811 0.6913 -0.2487 0.7347 340.217 -1.48 -2.8607 3.2208 242.645 0.6064 -0.7743 0.9835 308.07 -2656.9

245 -0.6231 -2.6832 2.7546 256.927 0.6349 -0.2364 0.6775 339.578 -1.2603 -2.4487 2.754 242.766 0.4889 -0.6995 0.8534 304.946 -1732.3

250 -0.481 -2.2585 2.3092 257.977 0.5649 -0.2189 0.6058 338.819 -1.0476 -2.041 2.2942 242.829 0.3678 -0.6256 0.7257 300.454 -975.092

255 -0.3571 -1.8272 1.8618 258.943 0.4813 -0.1951 0.5193 337.936 -0.8395 -1.6331 1.8363 242.794 0.2425 -0.5511 0.6021 293.749 -389.55

260 -0.2493 -1.384 1.4063 259.789 0.384 -0.1636 0.4174 336.926 -0.634 -1.221 1.3758 242.558 0.1121 -0.4748 0.4879 283.284 15.7933

265 -0.1705 -1.0124 1.0267 260.441 0.2935 -0.1379 0.3243 334.841 -0.4644 -0.8749 0.9905 242.04 0.0007 -0.4098 0.4098 270.093 248.345

270 -0.0848 -0.5024 0.5095 260.416 0.163 -0.0808 0.1819 333.645 -0.2479 -0.4217 0.4892 239.549 -0.1484 -0.3222 0.3548 245.265 258.169

275 0.0519 0.3951 0.3984 82.5217 -0.1035 0.0535 0.1165 152.663 0.1555 0.3418 0.3755 65.5294 -0.1179 0.0683 0.1363 149.897 -261.98

280 0.1099 0.9718 0.978 83.5502 -0.2638 0.1447 0.3009 151.266 0.3742 0.8275 0.9082 65.6697 -0.2825 0.1708 0.3302 148.841 -842.745

285 0.1599 1.5928 1.6009 84.2668 -0.4393 0.2563 0.5086 149.742 0.5999 1.3371 1.4655 65.8378 -0.4543 0.2829 0.5352 148.09 -1724.6

290 0.2048 2.2707 2.2799 84.8458 -0.6307 0.3931 0.7432 148.067 0.8364 1.8783 2.0561 65.9961 -0.6345 0.4074 0.754 147.3 -2948.9

295 0.2482 3.0216 3.0318 85.3045 -0.8394 0.5613 1.0098 146.229 1.0887 2.4611 2.6912 66.1371 -0.8247 0.5477 0.99 146.413 -4570.3

300 0.295 3.8676 3.8789 85.6388 -1.0671 0.7691 1.3154 144.218 1.3634 3.0995 3.3861 66.2568 -1.0275 0.7086 1.2482 145.41 -6661.9

305 0.3521 4.8394 4.8522 85.8382 -1.3162 1.0273 1.6696 142.027 1.6698 3.8133 4.1629 66.3517 -1.2468 0.8966 1.5358 144.278 -9324.4

310 0.4299 5.9814 5.9969 85.889 -1.5902 1.351 2.0866 139.65 2.0218 4.6318 5.0539 66.4182 -1.4887 1.1213 1.8637 143.012 -12702

315 0.5437 7.3622 7.3823 85.7763 -1.8954 1.7623 2.5881 137.085 2.4411 5.6015 6.1103 66.4528 -1.7632 1.3972 2.2497 141.605 -17011

320 0.7296 9.1784 9.2073 85.4551 -2.2681 2.3217 3.2457 134.33 2.9998 6.8584 7.4858 66.3756 -2.0837 1.7749 2.7371 139.576 -22823

325 1.0052 11.4487 11.493 84.9822 -2.676 3.0357 4.0468 131.397 3.6836 8.4149 9.1859 66.3585 -2.4914 2.2399 3.3502 138.043 -30292

330 1.4638 14.6814 14.754 84.3061 -3.201 4.0539 5.1654 128.295 4.6676 10.6297 11.6093 66.2932 -3.0502 2.9119 4.2169 136.329 -40917

335 2.6179 21.7801 21.937 83.1461 -4.2096 6.2758 7.5569 123.852 6.831 15.5071 16.9449 66.2262 -4.2877 4.3884 6.1353 134.335 -63434

340 4.7284 33.9193 34.247 82.064 -5.9094 9.9447 11.568 120.72 10.6416 23.9777 26.2331 66.0677 -6.3534 6.9827 9.4405 132.298 -101910

345 11.8075 73.1268 74.074 80.8278 -11.288 21.5923 24.3649 117.6 23.0943 51.5334 56.4715 65.8608 -13.015 15.4237 20.1814 130.16 -224240

350 -79.535 -484.19 490.68 260.672 73.3959 -155.25 171.723 295.303 -153.787 -329.635 363.744 244.989 78.5826 -97.266 125.043 308.935 1493000

355 -11.259 -55.33 56.464 258.498 6.7313 -16.757 18.0586 291.885 -18.0129 -38.5909 42.5878 244.979 8.4471 -12.131 14.7822 304.851 170710

360 -5.5462 -23.164 23.818 256.535 2.2316 -6.7533 7.1125 288.286 -7.7863 -16.4171 18.17 244.626 3.2081 -5.4226 6.3006 300.609 70487

Appendix A2

Bearing forces (Cartesian components, resultant, and direction) on each joint, and driving torqure, when omega = 10, only the gravity forces are neglected

theta2

degree

F12x

/10.^4

N

F12y

/10.^4

N

F12

/10.^4

N

theta12

degree

F14x

/10.^4

N

F14y

/10.^4

N

F14

/10.^4

N

theta14

degree

F16x

/10.^4

N

F16y

/10.^4

N

F16

/10.^4

N

theta16

degree

0 3.7432 20.0673 20.4134 79.4339 3.249 -6.8408 7.5732 295.4053 3.4249 -5.6673 6.6217 301.1455

5 2.8046 13.0423 13.3404 77.8641 1.6149 -4.0746 4.383 291.6202 1.9637 -3.8103 4.2865 297.2646

10 2.2906 9.4565 9.7299 76.384 0.9374 -2.7553 2.9104 288.7887 1.2352 -2.8699 3.1244 293.2867

15 1.7851 6.9059 7.1329 75.5067 0.5747 -1.8433 1.9308 287.3161 1.0541 -2.0107 2.2703 297.665

20 1.6083 5.7256 5.9472 74.3098 0.404 -1.3955 1.4528 286.1453 0.8284 -1.717 1.9064 295.7579

25 1.5581 5.1035 5.336 73.0222 0.3127 -1.1257 1.1683 285.5252 0.6999 -1.5676 1.7167 294.0612

30 1.617 4.8613 5.1232 71.6011 0.264 -0.964 0.9995 285.3156 0.6313 -1.5164 1.6425 292.6038

35 1.7683 4.8824 5.1927 70.0907 0.2394 -0.8665 0.899 285.4429 0.6008 -1.5328 1.6464 291.4028

40 2.2401 5.5148 5.9524 67.893 0.2374 -0.9182 0.9484 284.4949 0.3406 -1.9126 1.9427 280.0977

45 2.5261 5.8171 6.3419 66.5269 0.237 -0.8676 0.8994 285.2781 0.3456 -1.9933 2.023 279.8368

50 2.8473 6.1859 6.8097 65.2841 0.244 -0.8258 0.8611 286.4596 0.3617 -2.0842 2.1154 279.8454

55 3.1861 6.5831 7.3136 64.1741 0.256 -0.7871 0.8277 288.0158 0.3854 -2.1741 2.208 280.0526

60 3.5267 6.9797 7.8201 63.1931 0.2711 -0.7488 0.7963 289.905 0.4145 -2.2546 2.2924 280.4166

65 3.8557 7.3537 8.3032 62.331 0.2877 -0.7094 0.7655 292.0759 0.4474 -2.3206 2.3634 280.9133

70 4.1618 7.6893 8.7433 61.5757 0.3044 -0.6686 0.7346 294.4758 0.4832 -2.3692 2.418 281.5278

75 4.4363 7.9754 9.1262 60.9153 0.3199 -0.6263 0.7032 297.0564 0.5209 -2.3995 2.4554 282.2493

80 4.6257 8.0227 9.2607 60.0333 0.2993 -0.4714 0.5584 302.416 0.5569 -2.4192 2.4824 282.9635

85 4.8243 8.1782 9.4951 59.4638 0.3002 -0.4083 0.5068 306.324 0.5983 -2.4216 2.4944 283.8777

90 4.9811 8.2767 9.66 58.9596 0.2965 -0.3463 0.4559 310.5684 0.64 -2.4092 2.4927 284.8758

95 5.0938 8.3172 9.7531 58.5152 0.288 -0.2863 0.4061 315.1648 0.681 -2.3832 2.4785 285.9469

100 5.1607 8.2995 9.7732 58.1262 0.2746 -0.2292 0.3577 320.1529 0.7204 -2.3446 2.4528 287.0793

105 5.1808 8.2236 9.7195 57.7893 0.2565 -0.1756 0.3109 325.6101 0.7571 -2.2946 2.4163 288.2605

110 5.1532 8.0894 9.5914 57.5018 0.2341 -0.1262 0.2659 331.6748 0.79 -2.2339 2.3695 289.476

115 5.1087 7.9024 9.4099 57.1183 0.2279 -0.1141 0.2549 333.4088 0.7829 -2.1188 2.2588 290.2808

120 4.9855 7.6469 9.1286 56.8971 0.2045 -0.0803 0.2197 338.5589 0.7951 -2.0289 2.1791 291.401

125 4.8097 7.3268 8.7644 56.7172 0.1799 -0.0525 0.1874 343.7438 0.7968 -1.9274 2.0856 292.4615

130 4.5766 6.9351 8.3091 56.5784 0.1553 -0.0306 0.1583 348.841 0.7851 -1.8132 1.9759 293.4129

135 4.2785 6.4596 7.7481 56.4819 0.1318 -0.0147 0.1326 353.6324 0.7561 -1.6842 1.8461 294.1759

140 3.9005 5.8777 7.0542 56.4316 0.1113 -0.0044 0.1113 357.724 0.7037 -1.5366 1.69 294.6059

145 3.4143 5.1469 6.1764 56.4411 0.0964 0.0007 0.0964 0.4149 0.6182 -1.3631 1.4967 294.3942

150 2.7607 4.1814 5.0105 56.5661 0.0938 0.0012 0.0939 0.7202 0.4814 -1.15 1.2467 292.7156

155 1.7992 2.7865 3.3169 57.1506 0.1233 -0.0029 0.1234 358.6383 0.2552 -0.8679 0.9046 286.3865

160 0.1171 0.4245 0.4403 74.575 0.2649 -0.0153 0.2654 356.6934 -0.1596 -0.4439 0.4717 250.2249

165 -5.3588 -6.7762 8.6391 231.6619 1.2445 -0.0492 1.2455 357.7347 -1.392 0.5613 1.5009 158.0409

170 -51.4126 -53.9836 74.5485 226.3974 19.6346 -1.4571 19.6886 355.7559 -7.4504 3.3769 8.1799 155.6178

175 -9.7169 17.972 20.4307 118.3988 24.3886 -2.831 24.5524 353.3787 7.6565 -10.8568 13.2851 305.1924

180 5.0831 14.4534 15.3211 70.6239 4.62 -0.6905 4.6713 351.499 3.5891 -4.0989 5.4481 311.2064

185 4.8203 11.2917 12.2775 66.8831 2.5413 -0.4454 2.5801 350.0589 2.6421 -2.8417 3.8802 312.9155

190 4.235 9.5681 10.4635 66.1252 1.8948 -0.3723 1.9311 348.8844 2.195 -2.3022 3.1809 313.6352

195 3.6991 8.4149 9.1921 66.2701 1.6137 -0.3447 1.6501 347.9433 1.9211 -1.9767 2.7565 314.1827

200 3.2316 7.5509 8.2134 66.8306 1.4699 -0.3347 1.5075 347.1734 1.7249 -1.7472 2.4552 314.632

205 2.8206 6.8524 7.4102 67.6269 1.3866 -0.3324 1.4259 346.5176 1.5689 -1.5695 2.2192 314.9889

210 2.4555 6.2561 6.7207 68.5701 1.3302 -0.3335 1.3714 345.9265 1.4351 -1.4232 2.0211 315.2397

215 2.0526 5.3993 5.7763 69.185 1.1791 -0.2907 1.2144 346.1507 1.2175 -1.2313 1.7316 314.6767

220 1.7649 4.9266 5.2332 70.2903 1.1398 -0.2912 1.1765 345.6678 1.1057 -1.124 1.5767 314.5288

225 1.5078 4.4867 4.7333 71.4239 1.0955 -0.2906 1.1334 345.1458 0.9981 -1.0273 1.4323 314.1754

230 1.2781 4.0693 4.2653 72.564 1.0432 -0.2882 1.0823 344.5586 0.8922 -0.9382 1.2947 313.5598

235 1.0728 3.6668 3.8206 73.6916 0.9813 -0.2835 1.0215 343.8847 0.7859 -0.8547 1.1611 312.5997

240 0.8899 3.2729 3.3917 74.7891 0.9088 -0.276 0.9498 343.1042 0.6776 -0.7749 1.0294 311.169

245 0.7272 2.882 2.9723 75.8392 0.8252 -0.265 0.8668 342.1948 0.566 -0.6974 0.8982 309.0646

250 0.5829 2.4894 2.5567 76.8215 0.7304 -0.2497 0.7719 341.1269 0.45 -0.6208 0.7667 305.9363

255 0.4554 2.0902 2.1392 77.7079 0.6242 -0.229 0.6648 339.8525 0.3285 -0.5438 0.6353 301.1326

260 0.3432 1.6796 1.7143 78.45 0.5065 -0.2018 0.5452 338.2802 0.2007 -0.4653 0.5067 293.3366

265 0.2553 1.3338 1.358 79.1662 0.4003 -0.183 0.4401 335.4356 0.0915 -0.3987 0.409 282.9332

270 0.1656 0.8613 0.8771 79.1158 0.2529 -0.1328 0.2856 332.2942 -0.0579 -0.3089 0.3143 259.3812

275 0.0239 0.0015 0.024 3.6599 -0.0276 -0.0071 0.0285 194.3724 -0.029 0.0836 0.0885 109.1379

280 -0.04 -0.5376 0.5391 265.7416 -0.1989 0.0739 0.2122 159.6292 -0.1966 0.1879 0.272 136.3054

285 -0.0969 -1.1216 1.1258 265.0635 -0.3824 0.1735 0.4199 155.6023 -0.3726 0.3015 0.4793 141.0211

290 -0.1493 -1.7637 1.77 265.1616 -0.579 0.2965 0.6505 152.8888 -0.558 0.4273 0.7028 142.5567

295 -0.2008 -2.4813 2.4894 265.3742 -0.7901 0.449 0.9087 150.3885 -0.7544 0.5688 0.9448 142.984

300 -0.2561 -3.2977 3.3076 265.5598 -1.0171 0.6393 1.2013 147.8499 -0.9641 0.7308 1.2098 142.8394

305 -0.322 -4.2452 4.2574 265.662 -1.2622 0.8779 1.5375 145.1793 -1.1907 0.9197 1.5045 142.32

310 -0.4088 -5.3708 5.3863 265.6471 -1.5282 1.1798 1.9306 142.3307 -1.44 1.1449 1.8397 141.513

315 -0.5322 -6.7465 6.7674 265.4895 -1.8192 1.5661 2.4004 139.2763 -1.7215 1.421 2.2323 140.4619

320 -0.7294 -8.5744 8.6054 265.138 -2.167 2.0947 3.0139 135.9724 -2.048 1.7979 2.7252 138.7215

325 -1.0223 -10.8884 10.9363 264.6364 -2.5306 2.7674 3.75 132.4403 -2.4583 2.2608 3.3398 137.3963

330 -1.5157 -14.2297 14.3102 263.92 -2.9674 3.7202 4.7588 128.5773 -3.0128 2.9265 4.2002 135.832

335 -2.8023 -21.7298 21.9098 262.6517 -3.6741 5.7392 6.8145 122.6266 -4.2126 4.3743 6.0729 133.9215

340 -5.4247 -35.2543 35.6692 261.2523 -4.513 8.9418 10.0161 116.7802 -6.1423 6.8643 9.2112 131.8231

345 -16.6799 -84.9218 86.5443 258.8877 -4.1818 17.8981 18.3802 103.1509 -11.7918 14.4873 18.6796 129.1435

350 -225.0498 -229.0346 321.0985 225.5028 405.1549 -280.994 493.06 325.2569 142.7457 -153.9177 209.9214 312.8433

355 5.4144 43.1008 43.4395 82.8399 11.5589 -18.0425 21.4275 302.6456 9.4542 -13.1157 16.1679 305.7852

360 3.7432 20.0673 20.4134 79.4339 3.249 -6.8408 7.5732 295.4053 3.4249 -5.6673 6.6217 301.1455

Appendix A2


theta2

degree

F32x

/10.^4

N

F32y

/10.^4

N

F32

/10.^4

N

theta32

degree

F43x

/10.^4

N

F43y

/10.^4

N

F43

/10.^4

N

theta43

degree

F53x

/10.^4

N

F53y

/10.^4

N

F53

/10.^4

N

theta53

degree

F65x

/10.^4

N

F65y

/10.^4

N

F65

/10.^4

N

theta65

degree

T/10.^3

N.m

0 -3.8374 -20.067 20.431 259.174 2.9361 -5.0329 5.8267 300.259 -7.4822 -15.6508 17.3474 244.449 3.5441 -4.9369 6.0773 305.674 61.0646

5 -2.8984 -13.051 13.368 257.478 1.5319 -3.1511 3.5037 295.926 -4.8953 -10.2131 11.3257 244.391 2.0724 -3.3745 3.9601 301.556 38.7928

10 -2.3833 -9.4728 9.768 255.878 0.9326 -2.1636 2.3561 293.318 -3.6815 -7.5169 8.37 243.906 1.3433 -2.5525 2.8844 297.757 27.1285

15 -1.8761 -6.9302 7.1797 254.853 0.6065 -1.4094 1.5344 293.285 -2.7944 -5.684 6.3338 243.82 1.1654 -1.7513 2.1036 303.642 18.8926

20 -1.6968 -5.7578 6.0027 253.58 0.4569 -1.0463 1.1417 293.589 -2.4304 -4.8559 5.4301 243.412 0.9444 -1.4899 1.764 302.368 14.6985

25 -1.6435 -5.1433 5.3995 252.279 0.3794 -0.8248 0.9078 294.703 -2.2732 -4.4563 5.0026 242.973 0.8206 -1.3607 1.589 301.093 12.071

30 -1.6986 -4.9084 5.194 250.911 0.3405 -0.6913 0.7706 296.222 -2.2676 -4.3551 4.9101 242.495 0.7562 -1.3235 1.5243 299.743 10.3507

35 -1.8454 -4.9364 5.2701 249.502 0.3231 -0.6102 0.6904 297.901 -2.3776 -4.4681 5.0613 241.982 0.729 -1.3507 1.5349 298.358 9.0839

40 -2.3123 -5.5753 6.0358 247.475 0.3264 -0.671 0.7462 295.943 -2.8294 -5.0523 5.7906 240.75 0.4711 -1.7398 1.8024 285.153 8.4738

45 -2.5927 -5.8837 6.4296 246.219 0.3299 -0.625 0.7067 297.826 -3.0954 -5.4136 6.2361 240.24 0.4773 -1.829 1.8902 284.627 7.0814

50 -2.9078 -6.2581 6.9006 245.078 0.3394 -0.5851 0.6764 300.117 -3.4024 -5.8352 6.7547 239.754 0.4936 -1.9281 1.9903 284.36 5.4624

55 -3.2401 -6.6603 7.4066 244.058 0.3528 -0.5469 0.6508 302.825 -3.7305 -6.2828 7.3068 239.3 0.5166 -2.026 2.0908 284.304 3.5483

60 -3.5738 -7.0612 7.9141 243.155 0.3682 -0.5084 0.6278 305.914 -4.0618 -6.7288 7.8597 238.883 0.5441 -2.1145 2.1834 284.431 1.3255

65 -3.8955 -7.439 8.3972 242.361 0.3842 -0.4692 0.6064 309.315 -4.3815 -7.1517 8.3871 238.506 0.575 -2.1884 2.2627 284.722 -1.1766

70 -4.194 -7.7778 8.8365 241.665 0.3994 -0.4291 0.5862 312.95 -4.677 -7.5354 8.8689 238.173 0.6082 -2.2448 2.3258 285.16 -3.8978

75 -4.4606 -8.0664 9.2176 241.058 0.4127 -0.3884 0.5668 316.74 -4.9386 -7.8685 9.29 237.886 0.643 -2.2828 2.3717 285.73 -6.7583

80 -4.6421 -8.1155 9.3493 240.23 0.3916 -0.2393 0.4589 328.573 -5.0797 -8.0686 9.5344 237.807 0.6753 -2.3103 2.407 286.294 -9.6229

85 -4.8325 -8.2721 9.5802 239.707 0.3894 -0.1805 0.4292 335.128 -5.2494 -8.2851 9.8082 237.642 0.7132 -2.3202 2.4273 287.088 -12.4555

90 -4.9811 -8.3709 9.7408 239.245 0.3821 -0.1242 0.4018 341.995 -5.3723 -8.4402 10.0049 237.523 0.7513 -2.3151 2.4339 287.979 -15.1575

95 -5.0856 -8.411 9.829 238.842 0.3697 -0.0713 0.3765 349.08 -5.4461 -8.5317 10.1218 237.448 0.7885 -2.2963 2.4279 288.951 -17.6472

100 -5.1444 -8.3922 9.8435 238.492 0.3521 -0.0228 0.3529 356.303 -5.4694 -8.5585 10.1569 237.419 0.8239 -2.2648 2.4101 289.991 -19.851

105 -5.1564 -8.3146 9.7837 238.194 0.3299 0.0208 0.3305 3.6076 -5.4417 -8.52 10.1096 237.434 0.8566 -2.2218 2.3812 291.083 -21.7048

110 -5.121 -8.1779 9.649 237.945 0.3034 0.0588 0.3091 10.9623 -5.3627 -8.4156 9.979 237.493 0.8852 -2.1678 2.3416 292.212 -23.1547

115 -5.0689 -7.9877 9.4603 237.601 0.2938 0.0581 0.2994 11.1879 -5.2845 -8.2175 9.77 237.256 0.8736 -2.0595 2.2371 292.986 -24.252

120 -4.9384 -7.7285 9.1716 237.422 0.2677 0.078 0.2788 16.2392 -5.1122 -7.9695 9.4682 237.321 0.8814 -1.9758 2.1634 294.041 -24.7733

125 -4.7556 -7.4039 8.7997 237.287 0.2417 0.0909 0.2583 20.613 -4.8887 -7.6479 9.0769 237.412 0.8786 -1.8799 2.0751 295.05 -24.7771

130 -4.5161 -7.0073 8.3365 237.199 0.2177 0.0973 0.2384 24.0748 -4.6116 -7.2463 8.5893 237.527 0.8627 -1.7706 1.9695 295.976 -24.2336

135 -4.2119 -6.5262 7.7673 237.163 0.1977 0.0976 0.2205 26.2853 -4.2755 -6.7532 7.9928 237.662 0.8299 -1.6452 1.8427 296.768 -23.1055

140 -3.8283 -5.9383 7.0653 237.191 0.1846 0.0933 0.2069 26.8127 -3.8696 -6.1476 7.2641 237.812 0.775 -1.4989 1.6874 297.341 -21.3307

145 -3.3371 -5.2009 6.1795 237.314 0.1834 0.0868 0.2029 25.3375 -3.3722 -5.3903 6.3582 237.97 0.6895 -1.3226 1.4915 297.535 -18.7888

150 -2.6791 -4.2285 5.0057 237.642 0.2035 0.0835 0.22 22.3138 -2.7381 -4.4025 5.1845 238.121 0.5587 -1.0979 1.2319 296.97 -15.2195

155 -1.7139 -2.8263 3.3054 238.768 0.2698 0.0969 0.2867 19.7585 -1.8644 -3.0088 3.5396 238.216 0.3531 -0.7829 0.8589 294.273 -9.9988

160 -0.0286 -0.4567 0.4576 266.414 0.4685 0.1717 0.499 20.1276 -0.4707 -0.7373 0.8747 237.447 0.0044 -0.2612 0.2613 270.976 -1.3357

165 5.4498 6.7518 8.6768 51.0909 1.4959 0.7438 1.6706 26.439 3.4062 5.6377 6.5868 58.8608 -0.8547 1.2837 1.5422 123.656 24.1378

170 51.5053 53.9672 74.601 46.3371 17.3147 8.8209 19.4321 26.9964 24.6567 40.0358 47.0194 58.3725 -1.469 11.909 11.9992 97.0321 188.943

175 9.8107 -17.98 20.483 298.619 17.75 7.2948 19.1905 22.3415 -17.4919 -31.0097 35.6029 240.574 13.024 -3.1205 13.3926 346.526 -51.9036

180 -4.9889 -14.453 15.29 250.957 3.0615 0.8216 3.1699 15.0226 -9.3716 -16.2408 18.7507 240.013 4.3477 -3.009 5.2874 325.314 -43.9816

185 -4.7264 -11.284 12.233 247.272 1.6276 0.2079 1.6409 7.2807 -6.8613 -11.9502 13.7799 240.137 2.9587 -2.3852 3.8004 321.125 -32.9515

190 -4.1422 -9.5518 10.411 246.556 1.2145 0.0078 1.2145 0.3683 -5.6125 -9.8452 11.3326 240.314 2.3713 -2.0403 3.1282 319.29 -26.4356

195 -3.6082 -8.3905 9.1335 246.731 1.0528 -0.0925 1.0568 354.98 -4.8049 -8.4951 9.7598 240.507 2.03 -1.8032 2.7152 318.387 -21.8207

200 -3.1431 -7.5187 8.1492 247.314 0.983 -0.1552 0.9952 351.03 -4.211 -7.5043 8.6051 240.701 1.793 -1.623 2.4185 317.849 -18.2285

205 -2.7352 -6.8126 7.3412 248.125 0.9521 -0.1991 0.9727 348.191 -3.7383 -6.7134 7.684 240.889 1.6082 -1.4767 2.1833 317.44 -15.2708

210 -2.3739 -6.209 6.6473 249.076 0.9369 -0.2315 0.965 346.122 -3.3414 -6.0452 6.9072 241.069 1.452 -1.3525 1.9843 317.033 -12.7507

215 -1.9755 -5.3452 5.6986 249.717 0.839 -0.2398 0.8726 344.048 -2.8151 -5.1312 5.8527 241.249 1.2104 -1.191 1.6981 315.463 -9.876

220 -1.6928 -4.8661 5.1521 250.819 0.8275 -0.2547 0.8658 342.895 -2.5167 -4.6153 5.2569 241.396 1.0836 -1.0954 1.5408 314.691 -8.0321

225 -1.4413 -4.4201 4.6491 251.94 0.8086 -0.2644 0.8507 341.893 -2.2456 -4.1402 4.71 241.525 0.9628 -1.0083 1.3942 313.676 -6.4096

230 -1.2175 -3.9972 4.1785 253.06 0.7799 -0.2698 0.8253 340.919 -1.9951 -3.6946 4.1989 241.631 0.8449 -0.9277 1.2547 312.325 -4.9804

235 -1.0188 -3.5897 3.7315 254.155 0.7401 -0.2713 0.7883 339.867 -1.7603 -3.27 3.7137 241.705 0.7277 -0.8517 1.1202 310.512 -3.7258

240 -0.8428 -3.1913 3.3007 255.206 0.6883 -0.2693 0.7391 338.632 -1.5374 -2.8595 3.2466 241.735 0.6097 -0.7789 0.9891 308.05 -2.6345

245 -0.6874 -2.7967 2.8799 256.192 0.6237 -0.2636 0.6771 337.087 -1.3234 -2.4576 2.7913 241.698 0.4893 -0.7081 0.8607 304.649 -1.7009

250 -0.5507 -2.4009 2.4632 257.082 0.5459 -0.254 0.6021 335.045 -1.1158 -2.0597 2.3425 241.555 0.3657 -0.6379 0.7353 299.823 -0.9241

255 -0.4311 -1.9992 2.0452 257.833 0.4547 -0.24 0.5142 332.175 -0.9122 -1.6613 1.8953 241.229 0.2377 -0.5674 0.6152 292.736 -0.3075

260 -0.3269 -1.5868 1.6202 258.36 0.3498 -0.2206 0.4136 327.768 -0.7108 -1.2587 1.4455 240.547 0.1047 -0.4951 0.5061 281.943 0.1411

265 -0.2471 -1.24 1.2644 258.732 0.2536 -0.2062 0.3268 320.887 -0.5441 -0.9197 1.0687 239.391 -0.0086 -0.4333 0.4333 268.858 0.42

270 -0.1656 -0.7672 0.7848 257.817 0.1143 -0.168 0.2032 304.248 -0.3309 -0.4766 0.5802 235.226 -0.1608 -0.3504 0.3855 245.347 0.504

275 -0.0321 0.0923 0.0977 109.192 -0.1606 -0.0549 0.1697 198.882 0.0698 0.2771 0.2858 75.8573 -0.1334 0.0353 0.138 165.167 0.0729

280 0.0237 0.6303 0.6308 87.8489 -0.329 0.0129 0.3293 177.76 0.2863 0.7535 0.806 69.1942 -0.3011 0.1328 0.3291 156.199 -0.404

285 0.0725 1.2126 1.2147 86.5783 -0.5121 0.0993 0.5217 169.03 0.5104 1.2541 1.354 67.8543 -0.4761 0.2398 0.5331 153.264 -1.1681

290 0.1171 1.8522 1.8559 86.383 -0.7108 0.2096 0.7411 163.573 0.7459 1.7868 1.9362 67.3426 -0.6594 0.3591 0.7509 151.426 -2.2625

295 0.161 2.5667 2.5717 86.4114 -0.9264 0.3507 0.9905 159.266 0.9976 2.3619 2.5639 67.1019 -0.8528 0.4943 0.9857 149.9 -3.7447

300 0.209 3.3792 3.3857 86.4612 -1.1606 0.5316 1.2765 155.392 1.2722 2.9934 3.2525 66.9747 -1.0586 0.6502 1.2423 148.443 -5.6922

305 0.268 4.3223 4.3306 86.4518 -1.4158 0.7642 1.6089 151.642 1.5789 3.7013 4.024 66.8979 -1.2807 0.8333 1.5279 146.951 -8.2122

310 0.3483 5.4429 5.454 86.3388 -1.6957 1.0651 2.0025 147.866 1.9316 4.5155 4.9113 66.8406 -1.5252 1.0532 1.8535 145.373 -11.4582

315 0.4656 6.8131 6.829 86.0904 -2.0063 1.4585 2.4804 143.986 2.3516 5.4829 5.9659 66.7852 -1.8019 1.3248 2.2365 143.676 -15.6617

320 0.6572 8.6349 8.6599 85.6475 -2.3829 2.0075 3.1158 139.888 2.9108 6.7402 7.3419 66.6426 -2.1244 1.6982 2.7197 141.361 -21.4141

325 0.9451 10.9424 10.983 85.0634 -2.7921 2.7256 3.9019 135.69 3.5957 8.3038 9.0489 66.5863 -2.5318 2.1611 3.3287 139.517 -28.9256

330 1.4341 14.2768 14.349 84.2637 -3.3095 3.778 5.0226 131.218 4.5811 10.5388 11.4915 66.5058 -3.0866 2.8345 4.1906 137.438 -39.806

335 2.7169 21.7696 21.939 82.8861 -4.266 6.1614 7.4941 124.698 6.7501 15.5024 16.9082 66.4705 -4.2991 4.3331 6.1039 134.774 -63.5324

340 5.3362 35.2865 35.688 81.4006 -5.7314 10.4775 11.9426 118.68 10.6003 24.2787 26.492 66.4134 -6.2655 7.0372 9.4222 131.68 -106.455

345 16.589 84.9461 86.551 78.9499 -9.1417 27.2994 28.7894 108.514 23.4889 54.214 59.0837 66.5747 -12.094 16.49 20.4499 126.258 -262.748

350 224.957 229.051 321.05 45.5166 217.442 213.734 304.898 44.5073 -113.048 -163.785 199.011 235.386 140.549 -16.53 141.518 353.292 -805.283

355 -5.5082 -43.093 43.443 262.716 9.3449 -10.184 13.8218 312.539 -17.1067 -35.6775 39.5667 244.383 9.617 -10.53 14.2603 312.407 132.093

360 -3.8374 -20.067 20.431 259.174 2.9361 -5.0329 5.8267 300.259 -7.4822 -15.6508 17.3474 244.449 3.5441 -4.9369 6.0773 305.674 61.0646

Appendix A3

Bearing forces (Cartesian components, resultant, and direction) on each joint, and driving torqure, when omega = 10, only the inertial effects are neglected

theta2

degree

F12x

/10.^4

N

F12y

/10.^4

N

F12

/10.^4

N

theta12

degree

F14x

/10.^4

N

F14y

/10.^4

N

F14

/10.^4

N

theta14

degree

F16x

/10.^4

N

F16y

/10.^4

N

F16

/10.^4

N

theta16

degree

0 3.7231 19.9064 20.2516 79.4062 3.2585 -6.8386 7.5753 295.4771 3.4354 -5.7138 6.6671 301.0164

5 2.7738 12.8919 13.187 77.8573 1.6358 -4.0942 4.4089 291.7785 1.9735 -3.8457 4.3225 297.166

10 2.2569 9.3145 9.5841 76.3797 0.9613 -2.7877 2.9488 289.027 1.2449 -2.9008 3.1567 293.2258

15 1.7512 6.7719 6.9947 75.5009 0.5991 -1.8856 1.9785 287.6249 1.0636 -2.0397 2.3004 297.5397

20 1.5753 5.5989 5.8163 74.2857 0.4276 -1.4459 1.5078 286.4762 0.8379 -1.745 1.9358 295.6474

25 1.5261 4.9826 5.2111 72.9705 0.3353 -1.1825 1.2291 285.8333 0.7093 -1.5952 1.7458 293.9716

30 1.5859 4.745 5.003 71.519 0.2858 -1.0256 1.0647 285.571 0.6407 -1.5437 1.6714 292.5396

35 1.7374 4.7692 5.0758 69.983 0.2608 -0.9315 0.9673 285.6411 0.6102 -1.5599 1.675 291.3655

40 2.2088 5.4034 5.8374 67.7661 0.2591 -0.9853 1.0188 284.7309 0.3502 -1.9393 1.9707 280.2364

45 2.4936 5.7065 6.2275 66.3955 0.2596 -0.9359 0.9712 285.5046 0.3555 -2.0196 2.0507 279.9828

50 2.8129 6.0751 6.6947 65.1551 0.2682 -0.8944 0.9338 286.6912 0.3719 -2.1101 2.1426 279.9963

55 3.1491 6.4716 7.1971 64.052 0.2823 -0.8555 0.9009 288.2644 0.396 -2.1994 2.2348 280.2076

60 3.4867 6.8669 7.7014 63.0804 0.3001 -0.8164 0.8698 290.1798 0.4256 -2.2794 2.3188 280.5757

65 3.8122 7.2393 8.1817 62.229 0.3196 -0.7761 0.8393 292.3835 0.4591 -2.3448 2.3893 281.0769

70 4.1145 7.5731 8.6187 61.4849 0.3395 -0.7341 0.8088 294.8206 0.4954 -2.3929 2.4436 281.6963

75 4.3849 7.8574 8.9981 60.8357 0.3585 -0.6904 0.778 297.4407 0.5336 -2.4225 2.4806 282.4231

80 4.5705 7.9042 9.1305 59.9616 0.3413 -0.5356 0.6351 302.5075 0.5701 -2.4417 2.5073 283.1421

85 4.7647 8.0578 9.3611 59.4036 0.3461 -0.4712 0.5847 306.2949 0.612 -2.4435 2.519 284.0612

90 4.9169 8.1544 9.5221 58.9111 0.3465 -0.4079 0.5352 310.3471 0.6542 -2.4306 2.5171 285.0641

95 5.0248 8.193 9.6111 58.4789 0.3422 -0.3465 0.487 314.646 0.6957 -2.404 2.5027 286.14

100 5.0869 8.1733 9.627 58.1027 0.3332 -0.2878 0.4403 319.1808 0.7356 -2.365 2.4768 287.2773

105 5.102 8.0953 9.569 57.7792 0.3197 -0.2327 0.3954 323.9496 0.7728 -2.3145 2.4401 288.4632

110 5.0693 7.9591 9.4364 57.5063 0.3019 -0.1817 0.3524 328.9617 0.8061 -2.2533 2.3932 289.6836

115 5.0196 7.77 9.2503 57.1367 0.3005 -0.1679 0.3442 330.8159 0.7995 -2.1378 2.2824 290.5037

120 4.8911 7.5123 8.9642 56.9331 0.2821 -0.1323 0.3116 334.8698 0.812 -2.0475 2.2026 291.6325

125 4.7097 7.1899 8.5952 56.7734 0.2627 -0.1026 0.282 338.6562 0.814 -1.9456 2.109 292.7032

130 4.4711 6.796 8.1349 56.6586 0.2433 -0.0789 0.2558 342.0392 0.8025 -1.831 1.9991 293.6676

135 4.1674 6.3181 7.5687 56.5914 0.2254 -0.0609 0.2335 344.869 0.7736 -1.7017 1.8693 294.4479

140 3.7837 5.7337 6.8696 56.5786 0.2104 -0.0485 0.2159 347.0123 0.7213 -1.5537 1.713 294.9031

145 3.2922 5.0004 5.9869 56.6396 0.2009 -0.0411 0.2051 348.4275 0.6357 -1.3801 1.5194 294.7322

150 2.6344 4.0327 4.8169 56.8449 0.2029 -0.0383 0.2065 349.3158 0.4987 -1.1671 1.2691 293.1353

155 1.6725 2.6362 3.122 57.608 0.2335 -0.0398 0.2368 350.3185 0.2718 -0.8859 0.9267 287.056

160 0.0045 0.2749 0.2749 89.0526 0.3622 -0.0494 0.3655 352.2382 -0.1443 -0.4655 0.4873 252.7788

165 -5.3415 -6.9087 8.7328 232.2906 1.2146 -0.0789 1.2172 356.2844 -1.3795 0.5182 1.4736 159.4126

170 -49.0138 -53.8048 72.7826 227.6679 17.2102 -1.4649 17.2724 355.1347 -7.4248 3.0006 8.0082 157.9945

175 -6.8788 18.138 19.3985 110.7691 21.4474 -2.8363 21.6342 352.4667 7.7595 -11.2228 13.6441 304.6603

180 5.4579 14.3351 15.3389 69.1563 4.203 -0.7108 4.2627 350.4008 3.6313 -4.1656 5.5261 311.0798

185 4.9346 11.1425 12.1863 66.1131 2.3933 -0.4647 2.438 349.0116 2.6758 -2.8784 3.9301 312.9105

190 4.264 9.4072 10.3284 65.6168 1.8355 -0.3893 1.8763 348.0244 2.2254 -2.3294 3.2216 313.6916

195 3.6876 8.2468 9.0337 65.9079 1.5967 -0.3591 1.6366 347.3242 1.9497 -1.9994 2.7927 314.2782

200 3.1971 7.3774 8.0403 66.5701 1.4771 -0.3464 1.5172 346.8028 1.7523 -1.7672 2.4887 314.7564

205 2.7716 6.6742 7.2268 67.4479 1.4092 -0.3413 1.4499 346.3836 1.5952 -1.5876 2.2506 315.137

210 2.3971 6.0737 6.5296 68.4627 1.3632 -0.3396 1.4048 346.0122 1.4606 -1.4399 2.0511 315.409

215 1.9827 5.2119 5.5763 69.1725 1.2246 -0.2933 1.2593 346.5302 1.2419 -1.2466 1.7596 314.8908

220 1.6916 4.7357 5.0288 70.3432 1.1895 -0.2911 1.2246 346.2477 1.1293 -1.1385 1.6036 314.7679

225 1.4327 4.2926 4.5253 71.5427 1.1477 -0.2878 1.1833 345.9209 1.021 -1.0411 1.4582 314.4425

230 1.2023 3.8722 4.0546 72.7504 1.0968 -0.283 1.1327 345.532 0.9144 -0.9515 1.3197 313.8606

235 0.9975 3.467 3.6076 73.9491 1.0352 -0.276 1.0714 345.0691 0.8074 -0.8675 1.1851 312.9442

240 0.8156 3.0705 3.1769 75.1236 0.9623 -0.2664 0.9985 344.5246 0.6984 -0.7873 1.0525 311.5743

245 0.6547 2.6773 2.7562 76.2595 0.8776 -0.2534 0.9135 343.8942 0.5861 -0.7095 0.9203 309.5601

250 0.5126 2.2825 2.3394 77.3424 0.7812 -0.2362 0.8162 343.1769 0.4694 -0.6326 0.7878 306.5752

255 0.3878 1.8813 1.9209 78.3541 0.673 -0.2138 0.7062 342.3777 0.3473 -0.5554 0.6551 302.0167

260 0.2784 1.4689 1.495 79.2662 0.553 -0.1849 0.5831 341.5146 0.219 -0.4767 0.5245 294.6737

265 0.1941 1.1216 1.1383 80.1818 0.4437 -0.1648 0.4733 339.6249 0.1093 -0.4099 0.4242 284.9301

270 0.1074 0.6473 0.6561 80.5749 0.2938 -0.113 0.3148 338.965 -0.0407 -0.3199 0.3225 262.7552

275 -0.0312 -0.2144 0.2167 261.7198 0.0107 0.0144 0.018 53.2699 -0.0122 0.0729 0.0739 99.5102

280 -0.0921 -0.7555 0.7611 263.0507 -0.1633 0.097 0.19 149.2924 -0.1802 0.1774 0.2528 135.4556

285 -0.1459 -1.3415 1.3494 263.7924 -0.3495 0.1983 0.4019 150.4247 -0.3565 0.2912 0.4603 140.7523

290 -0.1954 -1.9857 1.9953 264.3791 -0.5488 0.3232 0.6369 149.5041 -0.5422 0.4173 0.6842 142.4138

295 -0.2442 -2.7056 2.7165 264.8428 -0.7623 0.4777 0.8996 147.9254 -0.7388 0.5591 0.9265 142.8804

300 -0.297 -3.5243 3.5368 265.1827 -0.9917 0.67 1.1968 145.9552 -0.9486 0.7214 1.1918 142.7492

305 -0.3608 -4.4743 4.4888 265.3896 -1.2388 0.9108 1.5376 143.6754 -1.1753 0.9106 1.4868 142.2337

310 -0.4458 -5.6024 5.6201 265.4505 -1.5066 1.215 1.9354 141.1163 -1.4246 1.1362 1.8222 141.4271

315 -0.5678 -6.9808 7.0039 265.3503 -1.7991 1.6036 2.41 138.2883 -1.7061 1.4126 2.215 140.3753

320 -0.7639 -8.8117 8.8447 265.0456 -2.1481 2.1348 3.0285 135.1787 -2.0323 1.7898 2.7081 138.6317

325 -1.0559 -11.1291 11.1791 264.5802 -2.513 2.8107 3.7703 131.7989 -2.4423 2.253 3.3228 137.3087

330 -1.5481 -14.4754 14.5579 263.8954 -2.9517 3.7683 4.7867 128.0711 -2.9961 2.9188 4.1828 135.7484

335 -2.8304 -21.9902 22.1716 262.6657 -3.6649 5.8028 6.8632 122.275 -4.1938 4.3657 6.0537 133.849

340 -5.4374 -35.549 35.9624 261.3037 -4.5244 9.0457 10.1141 116.5728 -6.1183 6.8498 9.1844 131.7713

345 -16.5809 -85.4066 87.0012 259.0132 -4.3329 18.2513 18.7585 103.355 -11.7397 14.4138 18.5897 129.1619

350 -218.3912 -236.3495 321.8009 227.2615 397.3634 -268.8781 479.7845 325.9155 143.8786 -158.9239 214.3778 312.1555

355 5.4725 42.8828 43.2306 82.7275 11.4818 -17.9126 21.2766 302.6593 9.4732 -13.2327 16.2741 305.5985

360 3.7231 19.9064 20.2516 79.4062 3.2585 -6.8386 7.5753 295.4771 3.4354 -5.7138 6.6671 301.0164

Appendix A3


theta2

degree

F32x

/10.^4

N

F32y

/10.^4

N

F32

/10.^4

N

theta32

degree

F43x

/10.^4

N

F43y

/10.^4

N

F43

/10.^4

N

theta43

degree

F53x

/10.^4

N

F53y

/10.^4

N

F53

/10.^4

N

theta53

degree

F65x

/10.^4

N

F65y

/10.^4

N

F65

/10.^4

N

theta65

degree

T/10.^3

N.m

0 -3.8173 -19.944 20.306 259.165 2.9456 -4.9798 5.7858 300.605 -7.4716 -15.6433 17.336 244.47 3.5547 -4.9505 6.0945 305.68 60.595

5 -2.8677 -12.938 13.252 257.502 1.5527 -3.1197 3.4848 296.46 -4.8854 -10.1944 11.3046 244.395 2.0823 -3.377 3.9673 301.658 38.3651

10 -2.3497 -9.3684 9.6585 255.92 0.9566 -2.1451 2.3487 294.033 -3.6718 -7.4937 8.345 243.896 1.353 -2.5505 2.8872 297.945 26.7405

15 -1.8422 -6.8338 7.0777 254.913 0.6309 -1.4008 1.5364 294.245 -2.7849 -5.659 6.3071 243.798 1.1749 -1.7474 2.1057 303.917 18.5448

20 -1.6638 -5.6686 5.9077 253.643 0.4805 -1.0457 1.1509 294.678 -2.4209 -4.8299 5.4027 243.378 0.9538 -1.4851 1.765 302.709 14.3891

25 -1.6115 -5.0599 5.3103 252.334 0.402 -0.8307 0.9228 295.827 -2.2639 -4.4299 4.9748 242.931 0.8299 -1.3554 1.5893 301.48 11.7969

30 -1.6675 -4.8296 5.1093 250.952 0.3623 -0.702 0.79 297.296 -2.2583 -4.3283 4.882 242.447 0.7656 -1.3179 1.5241 300.152 10.1088

35 -1.8146 -4.8607 5.1884 249.529 0.3445 -0.6243 0.713 298.892 -2.3681 -4.4411 5.033 241.932 0.7385 -1.3449 1.5343 298.771 8.8718

40 -2.281 -5.5014 5.9555 247.481 0.3481 -0.6872 0.7704 296.865 -2.8198 -5.0249 5.762 240.701 0.4807 -1.7336 1.799 285.499 8.2905

45 -2.5602 -5.8105 6.3496 246.221 0.3525 -0.6423 0.7327 298.757 -3.0856 -5.3859 6.2071 240.192 0.4872 -1.8224 1.8864 284.968 6.9272

50 -2.8734 -6.1848 6.8197 245.081 0.3636 -0.6028 0.7039 301.098 -3.3922 -5.807 6.7252 239.708 0.5038 -1.921 1.986 284.695 5.3387

55 -3.2031 -6.5862 7.3238 244.064 0.3791 -0.5643 0.6798 303.893 -3.7198 -6.254 7.2767 239.256 0.5272 -2.0184 2.0861 284.638 3.4571

60 -3.5338 -6.9859 7.8288 243.168 0.3972 -0.5252 0.6585 307.097 -4.0507 -6.6995 7.8289 238.841 0.5552 -2.1064 2.1783 284.767 1.2693

65 -3.852 -7.3621 8.309 242.381 0.4161 -0.485 0.639 310.632 -4.3699 -7.1218 8.3556 238.467 0.5866 -2.1797 2.2572 285.063 -1.1952

70 -4.1467 -7.6991 8.7448 241.694 0.4346 -0.4437 0.6211 314.406 -4.6649 -7.505 8.8366 238.136 0.6204 -2.2356 2.32 285.509 -3.8766

75 -4.4093 -7.9859 9.1223 241.095 0.4514 -0.4017 0.6042 318.334 -4.9259 -7.8375 9.257 237.85 0.6557 -2.273 2.3657 286.091 -6.6952

80 -4.5869 -8.0344 9.2515 240.278 0.4336 -0.2526 0.5018 329.775 -5.0665 -8.037 9.5006 237.773 0.6885 -2.2999 2.4007 286.666 -9.5168

85 -4.7729 -8.1891 9.4785 239.765 0.4353 -0.1925 0.476 336.138 -5.2357 -8.253 9.7736 237.609 0.727 -2.3092 2.4209 287.475 -12.305

90 -4.9169 -8.2861 9.6351 239.315 0.4321 -0.1349 0.4526 342.667 -5.3581 -8.4075 9.9697 237.491 0.7655 -2.3036 2.4275 288.382 -14.9621

95 -5.0166 -8.3243 9.719 238.925 0.4239 -0.0806 0.4315 349.239 -5.4314 -8.4985 10.0858 237.417 0.8032 -2.2843 2.4214 289.373 -17.4069

100 -5.0705 -8.3035 9.7293 238.59 0.4107 -0.0305 0.4119 355.752 -5.4542 -8.5248 10.1203 237.389 0.8391 -2.2523 2.4036 290.434 -19.5665

105 -5.0776 -8.2238 9.665 238.308 0.393 0.0146 0.3933 2.1241 -5.426 -8.4858 10.0723 237.404 0.8722 -2.2088 2.3748 291.549 -21.3773

110 -5.0371 -8.0851 9.5258 238.077 0.3713 0.0541 0.3752 8.2977 -5.3466 -8.3809 9.9411 237.464 0.9013 -2.1543 2.3353 292.702 -22.7859

115 -4.9798 -7.8928 9.3325 237.751 0.3664 0.0552 0.3705 8.5702 -5.268 -8.1825 9.7316 237.226 0.8901 -2.0457 2.231 293.515 -23.8443

120 -4.844 -7.6314 9.0389 237.595 0.3453 0.0768 0.3537 12.5448 -5.0953 -7.934 9.4293 237.291 0.8982 -1.9615 2.1574 294.604 -24.3295

125 -4.6557 -7.3046 8.6621 237.488 0.3245 0.0916 0.3372 15.7681 -4.8716 -7.612 9.0374 237.381 0.8958 -1.8652 2.0692 295.652 -24.3005

130 -4.4106 -6.9056 8.194 237.434 0.3058 0.0999 0.3217 18.0919 -4.5942 -7.21 8.5493 237.495 0.8801 -1.7555 1.9637 296.625 -23.7283

135 -4.1008 -6.4221 7.6197 237.44 0.2912 0.1023 0.3087 19.3531 -4.258 -6.7165 7.9525 237.627 0.8475 -1.6297 1.8369 297.474 -22.5758

140 -3.7116 -5.8317 6.9127 237.525 0.2837 0.1001 0.3009 19.4334 -3.852 -6.1106 7.2234 237.774 0.7926 -1.4831 1.6816 298.121 -20.7819

145 -3.2151 -5.0919 6.022 237.732 0.2879 0.0959 0.3035 18.4191 -3.3547 -5.3531 6.3174 237.926 0.7071 -1.3067 1.4857 298.419 -18.227

150 -2.5528 -4.1172 4.8444 238.2 0.3126 0.095 0.3267 16.9002 -2.7209 -4.3655 5.144 238.066 0.5759 -1.0821 1.2258 298.023 -14.6528

155 -1.5871 -2.7135 3.1436 239.677 0.38 0.1109 0.3958 16.2729 -1.8478 -2.9727 3.5002 238.136 0.3697 -0.7681 0.8524 295.701 -9.4393

160 0.084 -0.3446 0.3546 283.693 0.5658 0.1885 0.5964 18.4304 -0.4554 -0.7048 0.8391 237.134 0.0198 -0.2499 0.2507 274.523 -0.8094

165 5.4324 6.8468 8.7401 51.5707 1.466 0.7651 1.6536 27.5591 3.4187 5.6487 6.6027 58.8171 -0.8422 1.2735 1.5268 123.477 24.4944

170 49.1065 53.7509 72.805 47.5854 14.8903 8.8639 17.3288 30.7646 24.6823 39.7137 46.7589 58.1388 -1.4434 11.5657 11.6554 97.1139 187.12

175 6.9726 -18.184 19.475 290.98 14.8088 7.3404 16.5282 26.3667 -17.3889 -31.3215 35.8247 240.962 13.127 -3.4535 13.5737 345.26 -53.1793

180 -5.3637 -14.373 15.341 249.535 2.6445 0.8522 2.7784 17.8625 -9.3294 -16.2534 18.7406 240.144 4.3899 -3.0427 5.3413 325.273 -43.6416

185 -4.8408 -11.172 12.176 246.573 1.4796 0.2396 1.4988 9.1967 -6.8276 -11.9329 13.7481 240.223 2.9924 -2.3891 3.8291 321.397 -32.4887

190 -4.1712 -9.4283 10.31 246.135 1.1552 0.0417 1.1559 2.0653 -5.5821 -9.8183 11.2942 240.38 2.4016 -2.0347 3.1477 319.729 -25.9576

195 -3.5967 -8.2599 9.009 246.47 1.0357 -0.056 1.0373 356.903 -4.7764 -8.4637 9.7184 240.562 2.0586 -1.793 2.7299 318.945 -21.3549

200 -3.1086 -7.3827 8.0104 247.166 0.9902 -0.116 0.997 353.32 -4.1837 -7.4702 8.5619 240.749 1.8203 -1.6101 2.4302 318.507 -17.7868

205 -2.6863 -6.6718 7.1923 248.069 0.9747 -0.1571 0.9872 350.845 -3.7119 -6.6774 7.6398 240.931 1.6346 -1.462 2.193 318.19 -14.8603

210 -2.3155 -6.0641 6.4911 249.101 0.9698 -0.1867 0.9876 349.105 -3.3159 -6.0078 6.8622 241.105 1.4775 -1.3364 1.9922 317.872 -12.3762

215 -1.9055 -5.1954 5.5338 249.858 0.8845 -0.1916 0.905 347.78 -2.7908 -5.0924 5.807 241.276 1.2347 -1.1734 1.7033 316.46 -9.5474

220 -1.6195 -4.7127 4.9832 251.035 0.8771 -0.2037 0.9005 346.929 -2.4931 -4.5757 5.2108 241.416 1.1073 -1.077 1.5447 315.795 -7.7458

225 -1.3661 -4.2634 4.477 252.233 0.8608 -0.2108 0.8862 346.241 -2.2227 -4.1 4.6637 241.537 0.9857 -0.9893 1.3965 314.896 -6.1677

230 -1.1418 -3.8376 4.0038 253.431 0.8335 -0.2137 0.8604 345.618 -1.9729 -3.6538 4.1524 241.633 0.8671 -0.9081 1.2556 313.676 -4.7842

235 -0.9434 -3.4273 3.5548 254.609 0.794 -0.213 0.8221 344.986 -1.7388 -3.2287 3.6672 241.696 0.7492 -0.8316 1.1193 312.015 -3.5763

240 -0.7685 -3.0264 3.1225 255.751 0.7417 -0.2088 0.7705 344.28 -1.5166 -2.8178 3.2001 241.71 0.6304 -0.7585 0.9863 309.734 -2.5322

245 -0.6149 -2.6294 2.7004 256.839 0.6761 -0.2011 0.7053 343.435 -1.3033 -2.4157 2.7448 241.652 0.5095 -0.6873 0.8555 306.548 -1.646

250 -0.4804 -2.2315 2.2826 257.851 0.5968 -0.1897 0.6262 342.367 -1.0963 -2.0174 2.2961 241.48 0.3851 -0.6169 0.7272 301.977 -0.9166

255 -0.3634 -1.8279 1.8636 258.756 0.5036 -0.1739 0.5328 340.949 -0.8934 -1.6189 1.849 241.107 0.2566 -0.5461 0.6033 295.167 -0.3471

260 -0.2621 -1.4136 1.4377 259.496 0.3964 -0.1528 0.4248 338.917 -0.6925 -1.216 1.3994 240.338 0.123 -0.4736 0.4893 284.556 0.0548

265 -0.1859 -1.0653 1.0814 260.102 0.297 -0.1371 0.3271 335.219 -0.5264 -0.8769 1.0227 239.024 0.0091 -0.4116 0.4117 271.268 0.2892

270 -0.1074 -0.5906 0.6003 259.689 0.1553 -0.0973 0.1832 327.939 -0.3137 -0.4335 0.5351 234.111 -0.1436 -0.3285 0.3585 246.392 0.327

275 0.023 0.2707 0.2717 85.1451 -0.1223 0.0174 0.1235 171.891 0.0866 0.3204 0.3319 74.8706 -0.1165 0.0575 0.1299 153.756 -0.1497

280 0.0757 0.8107 0.8143 84.6636 -0.2934 0.0869 0.306 163.504 0.3027 0.7971 0.8526 69.2019 -0.2847 0.1552 0.3243 151.403 -0.6717

285 0.1215 1.395 1.4002 85.0206 -0.4792 0.1751 0.5102 159.934 0.5265 1.2979 1.4007 67.9196 -0.46 0.2625 0.5296 150.291 -1.4803

290 0.1632 2.0367 2.0433 85.4181 -0.6805 0.2872 0.7387 157.119 0.7617 1.8309 1.983 67.4108 -0.6436 0.3821 0.7484 149.305 -2.6187

295 0.2044 2.7534 2.761 85.7547 -0.8986 0.4303 0.9963 154.415 1.0132 2.4063 2.6109 67.1647 -0.8371 0.5175 0.9842 148.274 -4.1444

300 0.2499 3.5683 3.5771 85.9935 -1.1351 0.6132 1.2901 151.622 1.2877 3.0381 3.2997 67.0306 -1.0431 0.6737 1.2417 147.144 -6.135

305 0.3068 4.5139 4.5243 86.1118 -1.3924 0.848 1.6303 148.659 1.5943 3.7463 4.0715 66.9471 -1.2653 0.8571 1.5283 145.887 -8.6973

310 0.3853 5.6371 5.6502 86.0903 -1.6741 1.1512 2.0317 145.487 1.9469 4.5608 4.959 66.8833 -1.5098 1.0774 1.8548 144.489 -11.9847

315 0.5012 7.0099 7.0278 85.9107 -1.9862 1.5469 2.5175 142.089 2.3671 5.5285 6.014 66.8215 -1.7864 1.3493 2.2387 142.937 -16.2284

320 0.6917 8.8347 8.8618 85.5232 -2.3641 2.0985 3.1611 138.406 2.9265 6.7862 7.3903 66.6725 -2.1087 1.723 2.7232 140.748 -22.0195

325 0.9788 11.1457 11.189 84.9815 -2.7745 2.8198 3.9559 134.536 3.6118 8.3501 9.0977 66.6095 -2.5158 2.1862 3.333 139.01 -29.568

330 1.4666 14.485 14.559 84.2186 -3.2938 3.877 5.0872 130.351 4.5979 10.5852 11.5407 66.5215 -3.0699 2.8597 4.1955 137.03 -40.4854

335 2.745 21.9925 22.163 82.8853 -4.2568 6.276 7.5834 124.148 6.769 15.5479 16.9575 66.4735 -4.2802 4.3574 6.108 134.488 -64.2686

340 5.3489 35.5437 35.944 81.4419 -5.7429 10.6322 12.0841 118.375 10.6244 24.3184 26.5379 66.4001 -6.2414 7.0557 9.4201 131.496 -107.292

345 16.49 85.3935 86.971 79.0704 -9.2929 27.7035 29.2205 108.544 23.5411 54.1945 59.0866 66.5208 -12.042 16.4494 20.3863 126.207 -264.076

350 218.298 236.328 321.72 47.2711 209.65 225.9 308.195 47.1367 -111.915 -168.738 202.478 236.446 141.682 -21.504 143.305 351.37 -823.666

355 -5.5663 -42.912 43.272 262.609 9.2678 -10.003 13.6367 312.814 -17.0877 -35.7405 39.6153 244.447 9.636 -10.614 14.3353 312.236 131.467

360 -3.8173 -19.944 20.306 259.165 2.9456 -4.9798 5.7858 300.605 -7.4716 -15.6433 17.336 244.47 3.5547 -4.9505 6.0945 305.68 60.595

Appendix A4

Bearing forces (Cartesian components, resultant, and direction) on each joint, and driving torqure, when omega = 10, all are considered

theta2

degree

F12x

/10.^4

N

F12y

/10.^4

N

F12

/10.^4

N

theta12

degree

F14x

/10.^4

N

F14y

/10.^4

N

F14

/10.^4

N

theta14

degree

F16x

/10.^4

N

F16y

/10.^4

N

F16

/10.^4

N

theta16

degree

0 3.6929 19.8875 20.2275 79.4805 3.2846 -6.8529 7.5994 295.6088 3.4395 -5.6807 6.6408 301.1939

5 2.7544 12.8711 13.1626 77.9208 1.6504 -4.0952 4.4153 291.9498 1.9783 -3.8239 4.3053 297.3551

10 2.2411 9.2941 9.5605 76.4428 0.9721 -2.7842 2.949 289.2459 1.2499 -2.8838 3.1431 293.4331

15 1.7368 6.7517 6.9715 75.5738 0.6082 -1.8801 1.9761 287.9244 1.0689 -2.025 2.2898 297.8273

20 1.5615 5.579 5.7934 74.3636 0.436 -1.4394 1.504 286.85 0.8433 -1.7316 1.9261 295.967

25 1.5127 4.9632 5.1886 73.0499 0.3432 -1.1756 1.2247 286.2747 0.7149 -1.5826 1.7366 294.3089

30 1.5727 4.7263 4.9811 71.5944 0.2933 -1.0188 1.0602 286.0604 0.6463 -1.5318 1.6626 292.8765

35 1.7247 4.7515 5.0548 70.0502 0.2679 -0.925 0.9631 286.1536 0.6158 -1.5486 1.6666 291.6864

40 2.1966 5.3869 5.8175 67.816 0.2658 -0.9794 1.0148 285.1832 0.3557 -1.9288 1.9613 280.4494

45 2.4821 5.6913 6.209 66.4372 0.2659 -0.9305 0.9678 285.9464 0.3608 -2.0098 2.0419 280.1771

50 2.8021 6.0613 6.6777 65.1895 0.274 -0.8897 0.9309 287.115 0.3769 -2.101 2.1345 280.1713

55 3.1392 6.4592 7.1816 64.0803 0.2876 -0.8514 0.8987 288.6663 0.4007 -2.1911 2.2274 280.3638

60 3.4776 6.8558 7.6874 63.1038 0.3049 -0.8129 0.8682 290.5579 0.4299 -2.2719 2.3122 280.7145

65 3.8039 7.2295 8.1692 62.2483 0.324 -0.7731 0.8383 292.737 0.4629 -2.3381 2.3834 281.1996

70 4.1071 7.5646 8.6076 61.5009 0.3435 -0.7316 0.8082 295.1494 0.4988 -2.3868 2.4384 281.8045

75 4.3784 7.8499 8.9884 60.8489 0.3621 -0.6883 0.7777 297.7451 0.5367 -2.4172 2.476 282.5181

80 4.5648 7.8975 9.1219 59.9719 0.3444 -0.5337 0.6352 302.8348 0.5727 -2.4369 2.5033 283.2252

85 4.7597 8.052 9.3536 59.4117 0.3488 -0.4696 0.585 306.6044 0.6142 -2.4393 2.5155 284.1334

90 4.9127 8.1493 9.5156 58.9172 0.3489 -0.4065 0.5357 310.6377 0.656 -2.4269 2.514 285.1262

95 5.0213 8.1886 9.6055 58.4829 0.3442 -0.3452 0.4875 314.9166 0.6972 -2.4009 2.5 286.1928

100 5.0841 8.1694 9.6222 58.1046 0.3349 -0.2867 0.4408 319.4304 0.7367 -2.3623 2.4745 287.3215

105 5.0999 8.0919 9.565 57.7789 0.3209 -0.2316 0.3958 324.1778 0.7736 -2.3122 2.4382 288.4994

110 5.0679 7.9561 9.4331 57.5033 0.3027 -0.1806 0.3525 329.1698 0.8066 -2.2513 2.3915 289.7124

115 5.019 7.7673 9.2478 57.1306 0.3008 -0.1668 0.3439 330.9885 0.7998 -2.1362 2.281 290.5252

120 4.8914 7.5099 8.9624 56.9231 0.2817 -0.1312 0.3107 335.0247 0.8121 -2.0462 2.2015 291.6474

125 4.711 7.1877 8.594 56.7583 0.2615 -0.1014 0.2805 338.8011 0.8139 -1.9446 2.108 292.7123

130 4.4734 6.7938 8.1344 56.6368 0.2412 -0.0775 0.2534 342.1863 0.8023 -1.8302 1.9984 293.6716

135 4.1708 6.3159 7.5688 56.5606 0.2221 -0.0594 0.2299 345.0336 0.7734 -1.7011 1.8686 294.4485

140 3.7885 5.7315 6.8704 56.5355 0.2058 -0.0467 0.2111 347.2106 0.7211 -1.5533 1.7125 294.9032

145 3.2981 4.9979 5.988 56.5797 0.1951 -0.0391 0.199 348.6746 0.6357 -1.3796 1.519 294.7381

150 2.6405 4.0295 4.8176 56.764 0.1965 -0.0359 0.1997 349.6401 0.499 -1.1663 1.2686 293.1628

155 1.6754 2.6317 3.1197 57.5188 0.2296 -0.0372 0.2326 350.7983 0.2728 -0.884 0.9251 287.1516

160 -0.01 0.2664 0.2666 92.1493 0.3744 -0.0466 0.3773 352.9079 -0.1419 -0.4598 0.4812 252.846

165 -5.486 -6.9383 8.8451 231.6675 1.3539 -0.0765 1.356 356.7657 -1.3743 0.5454 1.4785 158.3521

170 -51.542 -54.1489 74.7575 226.413 19.7463 -1.4814 19.8017 355.7097 -7.4326 3.3612 8.1573 155.6662

175 -9.8479 17.8034 20.3456 118.949 24.5018 -2.8523 24.6673 353.36 7.6742 -10.8722 13.3079 305.2166

180 4.9514 14.2815 15.1155 70.8787 4.734 -0.7087 4.7868 351.4853 3.6068 -4.1141 5.4713 311.2408

185 4.6887 11.1166 12.0649 67.1313 2.6552 -0.4606 2.6949 350.1597 2.6598 -2.8567 3.9032 312.9559

190 4.1045 9.3898 10.2477 66.3891 2.0077 -0.3845 2.0442 349.1597 2.2127 -2.317 3.2038 313.6809

195 3.5706 8.2336 8.9745 66.5557 1.7247 -0.354 1.7607 348.4019 1.9387 -1.9914 2.7792 314.2326

200 3.1058 7.3667 7.9946 67.14 1.5782 -0.3412 1.6147 347.7992 1.7425 -1.7617 2.4778 314.6854

205 2.6983 6.6654 7.1909 67.9611 1.4914 -0.3364 1.5289 347.2881 1.5863 -1.5838 2.2416 315.0458

210 2.3373 6.0666 6.5012 68.9298 1.4311 -0.3351 1.4698 346.8217 1.4525 -1.4373 2.0434 315.3007

215 1.9366 5.2065 5.555 69.5965 1.2778 -0.2892 1.3102 347.2485 1.2347 -1.2453 1.7537 314.7555

220 1.6539 4.7316 5.0123 70.7335 1.2338 -0.2876 1.2669 346.8768 1.1228 -1.1379 1.5986 314.6181

225 1.402 4.2896 4.5129 71.9014 1.1844 -0.2851 1.2183 346.467 1.0151 -1.041 1.454 314.2791

230 1.1775 3.8705 4.0456 73.0793 1.127 -0.281 1.1615 346.0013 0.909 -0.9518 1.3161 313.6843

235 0.9776 3.4662 3.6015 74.2503 1.0599 -0.2747 1.0949 345.468 0.8026 -0.8681 1.1823 312.7547

240 0.7999 3.0707 3.1732 75.3996 0.9823 -0.2658 1.0176 344.8587 0.6942 -0.7882 1.0503 311.3706

245 0.6423 2.6784 2.7543 76.5138 0.8937 -0.2534 0.9289 344.1684 0.5824 -0.7106 0.9188 309.3397

250 0.5031 2.2843 2.3391 77.5795 0.7939 -0.2368 0.8285 343.395 0.4662 -0.6339 0.7869 306.3341

255 0.3805 1.8838 1.9218 78.5814 0.683 -0.2148 0.716 342.5411 0.3446 -0.5568 0.6548 301.7489

260 0.2729 1.4719 1.4969 79.4957 0.5609 -0.1864 0.591 341.6201 0.2167 -0.4782 0.525 294.3739

265 0.1898 1.1252 1.1411 80.4243 0.4499 -0.1667 0.4798 339.6716 0.1073 -0.4115 0.4253 284.6177

270 0.1041 0.6513 0.6596 80.9175 0.2988 -0.1153 0.3202 338.8989 -0.0423 -0.3217 0.3244 262.5061

275 -0.0339 -0.2098 0.2125 260.8209 0.0148 0.0116 0.0188 38.1965 -0.0136 0.071 0.0723 100.8356

280 -0.0944 -0.7501 0.7561 262.8249 -0.1598 0.0938 0.1853 149.6006 -0.1813 0.1753 0.2522 135.976

285 -0.1482 -1.3354 1.3436 263.6682 -0.3463 0.1945 0.3971 150.6766 -0.3575 0.289 0.4597 141.0488

290 -0.1978 -1.9786 1.9885 264.2905 -0.5455 0.3186 0.6317 149.7141 -0.543 0.4148 0.6834 142.6227

295 -0.2469 -2.6973 2.7086 264.7699 -0.7588 0.4722 0.8937 148.1076 -0.7396 0.5564 0.9255 143.044

300 -0.3002 -3.5146 3.5274 265.1177 -0.9877 0.6633 1.1898 146.117 -0.9494 0.7184 1.1906 142.8855

305 -0.3646 -4.4628 4.4777 265.3292 -1.2343 0.9027 1.5291 143.8209 -1.1761 0.9073 1.4854 142.3516

310 -0.4503 -5.5888 5.6069 265.3931 -1.5012 1.2049 1.925 141.2476 -1.4255 1.1326 1.8206 141.5316

315 -0.5732 -6.9646 6.9881 265.2951 -1.7927 1.5913 2.3971 138.4067 -1.707 1.4087 2.2132 140.4692

320 -0.7703 -8.792 8.8257 264.9926 -2.1405 2.1194 3.0122 135.2833 -2.0335 1.7855 2.7061 138.7163

325 -1.0638 -11.1049 11.1557 264.5281 -2.5035 2.7911 3.7493 131.8913 -2.4439 2.2484 3.3208 137.3852

330 -1.5582 -14.4443 14.5281 263.843 -2.9394 3.742 4.7584 128.1501 -2.9984 2.9141 4.1812 135.8167

335 -2.8465 -21.9403 22.1242 262.6078 -3.6443 5.7569 6.8134 122.335 -4.1982 4.3618 6.0539 133.9054

340 -5.4705 -35.4606 35.8801 261.2301 -4.4816 8.9554 10.0142 116.5848 -6.1279 6.8516 9.1922 131.8085

345 -16.7272 -85.1231 86.751 258.8827 -4.149 17.907 18.3814 103.0452 -11.7773 14.4746 18.6606 129.1337

350 -225.0983 -229.2303 321.2721 225.5211 405.1889 -280.9905 493.0859 325.2594 142.7602 -153.9307 209.9408 312.8438

355 5.365 42.9113 43.2454 82.8736 11.5936 -18.045 21.4485 302.7201 9.4688 -13.1289 16.1872 305.7999

360 3.6929 19.8875 20.2275 79.4805 3.2846 -6.8529 7.5994 295.6088 3.4395 -5.6807 6.6408 301.1939

Appendix A4


theta2

degree

F32x

/10.^4

N

F32y

/10.^4

N

F32

/10.^4

N

theta32

degree

F43x

/10.^4

N

F43y

/10.^4

N

F43

/10.^4

N

theta43

degree

F53x

/10.^4

N

F53y

/10.^4

N

F53

/10.^4

N

theta53

degree

F65x

/10.^4

N

F65y

/10.^4

N

F65

/10.^4

N

theta65

degree

T/10.^3

N.m

0 -3.7871 -19.925 20.282 259.238 2.9717 -4.994 5.8113 300.755 -7.4675 -15.6102 17.3044 244.435 3.5588 -4.9174 6.0701 305.894 60.5375

5 -2.8483 -12.917 13.227 257.565 1.5673 -3.1207 3.4922 296.667 -4.8806 -10.1726 11.2829 244.369 2.087 -3.3552 3.9513 301.883 38.3071

10 -2.3339 -9.3479 9.6349 255.982 0.9673 -2.1417 2.35 294.306 -3.6668 -7.4767 8.3275 243.876 1.358 -2.5335 2.8745 298.193 26.6876

15 -1.8278 -6.8136 7.0545 254.983 0.64 -1.3954 1.5351 294.639 -2.7796 -5.6443 6.2915 243.782 1.1802 -1.7327 2.0965 304.261 18.4968

20 -1.65 -5.6487 5.8847 253.717 0.4888 -1.0393 1.1485 295.19 -2.4155 -4.8165 5.3882 243.366 0.9592 -1.4717 1.7567 303.096 14.3465

25 -1.598 -5.0405 5.2878 252.409 0.4099 -0.8238 0.9202 296.453 -2.2583 -4.4173 4.9611 242.922 0.8355 -1.3429 1.5816 301.89 11.7607

30 -1.6543 -4.8109 5.0873 251.024 0.3698 -0.6952 0.7875 298.008 -2.2526 -4.3164 4.8689 242.441 0.7712 -1.306 1.5167 300.563 10.0796

35 -1.8018 -4.843 5.1673 249.592 0.3517 -0.6178 0.7109 299.647 -2.3625 -4.4298 5.0205 241.928 0.7441 -1.3336 1.5272 299.159 8.85

40 -2.2687 -5.4849 5.9356 247.529 0.3548 -0.6813 0.7681 297.513 -2.8143 -5.0143 5.7501 240.697 0.4863 -1.723 1.7903 285.759 8.276

45 -2.5486 -5.7954 6.331 246.261 0.3588 -0.637 0.7311 299.388 -3.0803 -5.376 6.1959 240.189 0.4925 -1.8125 1.8782 285.202 6.9194

50 -2.8626 -6.171 6.8026 245.114 0.3694 -0.5981 0.7029 301.699 -3.3872 -5.7979 6.7148 239.706 0.5088 -1.9119 1.9785 284.903 5.3369

55 -3.1932 -6.5738 7.3083 244.092 0.3844 -0.5602 0.6794 304.455 -3.7151 -6.2457 7.2671 239.255 0.5319 -2.0101 2.0793 284.821 3.4603

60 -3.5247 -6.9749 7.8149 243.191 0.402 -0.5217 0.6586 307.615 -4.0464 -6.6919 7.8202 238.84 0.5595 -2.0988 2.1721 284.927 1.2765

65 -3.8437 -7.3524 8.2965 242.4 0.4205 -0.482 0.6396 311.102 -4.366 -7.1151 8.3478 238.466 0.5905 -2.1729 2.2517 285.203 -1.185

70 -4.1393 -7.6906 8.7337 241.71 0.4385 -0.4412 0.622 314.829 -4.6614 -7.4989 8.8297 238.135 0.6238 -2.2295 2.3151 285.631 -3.8644

75 -4.4027 -7.9783 9.1125 241.109 0.4549 -0.3995 0.6055 318.708 -4.9229 -7.8321 9.2508 237.849 0.6587 -2.2676 2.3614 286.198 -6.6818

80 -4.5812 -8.0278 9.2429 240.288 0.4367 -0.2507 0.5036 330.137 -5.0639 -8.0322 9.4952 237.771 0.6911 -2.2951 2.3969 286.759 -9.5031

85 -4.7679 -8.1833 9.471 239.773 0.438 -0.1909 0.4778 336.447 -5.2335 -8.2488 9.7689 237.607 0.7292 -2.305 2.4176 287.555 -12.2915

90 -4.9127 -8.281 9.6286 239.322 0.4345 -0.1335 0.4545 342.924 -5.3563 -8.4038 9.9656 237.488 0.7673 -2.2999 2.4246 288.451 -14.9493

95 -5.0131 -8.3199 9.7135 238.929 0.4259 -0.0793 0.4332 349.45 -5.4299 -8.4953 10.0824 237.415 0.8047 -2.2811 2.4189 289.431 -17.3952

100 -5.0678 -8.2996 9.7245 238.592 0.4124 -0.0294 0.4134 355.924 -5.4531 -8.5221 10.1174 237.386 0.8403 -2.2496 2.4014 290.482 -19.5562

105 -5.0756 -8.2204 9.6611 238.307 0.3943 0.0156 0.3946 2.2706 -5.4252 -8.4835 10.0699 237.401 0.8731 -2.2064 2.3729 291.588 -21.3686

110 -5.0357 -8.0821 9.5225 238.074 0.372 0.0552 0.3761 8.4362 -5.3461 -8.3789 9.9392 237.461 0.9018 -2.1523 2.3336 292.734 -22.779

115 -4.9792 -7.8902 9.3299 237.745 0.3666 0.0563 0.3709 8.7264 -5.2677 -8.1809 9.7301 237.223 0.8904 -2.0441 2.2296 293.539 -23.8394

120 -4.8443 -7.629 9.037 237.585 0.3449 0.0779 0.3536 12.7359 -5.0952 -7.9327 9.4281 237.287 0.8983 -1.9602 2.1562 294.621 -24.3266

125 -4.657 -7.3023 8.6609 237.473 0.3233 0.0929 0.3364 16.0228 -4.8716 -7.611 9.0366 237.378 0.8957 -1.8642 2.0682 295.663 -24.2997

130 -4.4129 -6.9035 8.1934 237.412 0.3037 0.1013 0.3201 18.4423 -4.5944 -7.2093 8.5488 237.491 0.8799 -1.7547 1.963 296.631 -23.7295

135 -4.1042 -6.42 7.6198 237.41 0.288 0.1038 0.3061 19.8296 -4.2582 -6.716 7.9521 237.624 0.8472 -1.6292 1.8363 297.476 -22.5787

140 -3.7163 -5.8295 6.9133 237.482 0.2792 0.1019 0.2972 20.0503 -3.8522 -6.1102 7.2232 237.771 0.7924 -1.4827 1.6812 298.122 -20.786

145 -3.2209 -5.0894 6.023 237.672 0.2821 0.0979 0.2986 19.1478 -3.3547 -5.3527 6.3171 237.923 0.707 -1.3062 1.4853 298.426 -18.231

150 -2.5589 -4.1141 4.845 238.119 0.3062 0.0973 0.3213 17.6363 -2.7205 -4.3648 5.1432 238.065 0.5763 -1.0813 1.2253 298.054 -14.6538

155 -1.59 -2.709 3.1411 239.59 0.3761 0.1136 0.3928 16.8026 -1.8467 -2.9708 3.4981 238.134 0.3707 -0.7662 0.8511 295.819 -9.4305

160 0.0985 -0.3361 0.3503 286.332 0.578 0.1913 0.6088 18.316 -0.453 -0.6992 0.8331 237.059 0.0221 -0.2443 0.2453 275.171 -0.7702

165 5.5769 6.8764 8.8537 50.9574 1.6053 0.7674 1.7793 25.5517 3.4239 5.676 6.6287 58.9003 -0.8369 1.3007 1.5467 122.758 24.6953

170 51.6347 54.0951 74.783 46.333 17.4263 8.8475 19.5436 26.9173 24.6745 40.0743 47.0614 58.3786 -1.4513 11.9262 12.0142 96.938 189.488

175 9.9417 -17.849 20.431 299.117 17.8632 7.3244 19.3065 22.2951 -17.4742 -30.971 35.5605 240.568 13.0417 -3.103 13.4058 346.617 -51.3777

180 -4.8572 -14.319 15.12 251.262 3.1755 0.8543 3.2884 15.0579 -9.3539 -16.2019 18.7082 240.001 4.3654 -2.9913 5.292 325.58 -43.4786

185 -4.5949 -11.146 12.056 247.596 1.7415 0.2437 1.7585 7.9658 -6.8436 -11.9111 13.7372 240.12 2.9764 -2.3673 3.803 321.503 -32.4754

190 -4.0117 -9.411 10.23 246.912 1.3274 0.0465 1.3282 2.0076 -5.5949 -9.8059 11.2897 240.293 2.3889 -2.0222 3.1299 319.752 -25.99

195 -3.4796 -8.2467 8.9507 247.123 1.1638 -0.0509 1.1649 357.496 -4.7873 -8.4556 9.7168 240.483 2.0476 -1.7849 2.7164 318.921 -21.4082

200 -3.0173 -7.372 7.9656 247.741 1.0913 -0.1108 1.0969 354.201 -4.1935 -7.4646 8.5619 240.673 1.8105 -1.6045 2.4192 318.451 -17.8513

205 -2.6129 -6.6631 7.1571 248.588 1.057 -0.1522 1.0679 351.807 -3.7208 -6.6736 7.6408 240.858 1.6256 -1.4581 2.1838 318.109 -14.9305

210 -2.2557 -6.057 6.4634 249.574 1.0377 -0.1822 1.0536 350.043 -3.3241 -6.0052 6.8638 241.034 1.4694 -1.3337 1.9844 317.77 -12.4484

215 -1.8595 -5.1899 5.513 250.288 0.9377 -0.1874 0.9563 348.698 -2.7979 -5.0911 5.8093 241.208 1.2276 -1.172 1.6972 316.326 -9.6142

220 -1.5817 -4.7085 4.9671 251.431 0.9214 -0.2002 0.9429 347.743 -2.4997 -4.575 5.2133 241.349 1.1007 -1.0763 1.5395 315.643 -7.8099

225 -1.3354 -4.2605 4.4649 252.598 0.8975 -0.208 0.9213 346.951 -2.2286 -4.0998 4.6664 241.472 0.9798 -0.9891 1.3922 314.727 -6.2276

230 -1.1169 -3.8358 3.9951 253.765 0.8637 -0.2117 0.8893 346.228 -1.9783 -3.6541 4.1552 241.57 0.8617 -0.9084 1.2521 313.49 -4.8387

235 -0.9235 -3.4266 3.5489 254.916 0.8187 -0.2117 0.8456 345.505 -1.7436 -3.2293 3.67 241.634 0.7444 -0.8322 1.1166 311.812 -3.6246

240 -0.7528 -3.0266 3.1188 256.033 0.7617 -0.2081 0.7896 344.717 -1.5209 -2.8187 3.2028 241.65 0.6262 -0.7593 0.9842 309.512 -2.5741

245 -0.6025 -2.6305 2.6986 257.099 0.6921 -0.2011 0.7207 343.798 -1.307 -2.4167 2.7475 241.595 0.5058 -0.6884 0.8542 306.305 -1.6814

250 -0.4709 -2.2333 2.2824 258.094 0.6095 -0.1902 0.6385 342.666 -1.0995 -2.0187 2.2987 241.424 0.3819 -0.6181 0.7266 301.711 -0.9457

255 -0.3561 -1.8303 1.8646 258.99 0.5136 -0.175 0.5426 341.19 -0.8961 -1.6203 1.8516 241.054 0.2538 -0.5475 0.6034 294.875 -0.3705

260 -0.2566 -1.4166 1.4396 259.735 0.4043 -0.1543 0.4327 339.109 -0.6949 -1.2175 1.4018 240.286 0.1207 -0.4751 0.4902 284.248 0.0366

265 -0.1816 -1.0688 1.0842 260.357 0.3032 -0.139 0.3336 335.372 -0.5284 -0.8785 1.0251 238.976 0.0071 -0.4132 0.4132 270.99 0.2753

270 -0.1041 -0.5946 0.6037 260.068 0.1602 -0.0996 0.1887 328.146 -0.3153 -0.4353 0.5375 234.079 -0.1452 -0.3302 0.3608 246.264 0.3168

275 0.0257 0.2661 0.2673 84.4859 -0.1182 0.0147 0.1191 172.92 0.0853 0.3185 0.3297 75.0147 -0.1179 0.0556 0.1304 154.776 -0.1567

280 0.0781 0.8054 0.8092 84.4627 -0.2899 0.0837 0.3017 163.905 0.3016 0.795 0.8503 69.225 -0.2859 0.1531 0.3243 151.823 -0.6759

285 0.1238 1.3888 1.3943 84.9061 -0.476 0.1712 0.5058 160.217 0.5255 1.2957 1.3982 67.9221 -0.461 0.2602 0.5294 150.557 -1.4821

290 0.1656 2.0296 2.0364 85.335 -0.6773 0.2826 0.7339 157.352 0.7609 1.8284 1.9804 67.4063 -0.6444 0.3796 0.7479 149.502 -2.6182

295 0.2071 2.7451 2.7529 85.6856 -0.8951 0.4247 0.9908 154.617 1.0125 2.4035 2.6081 67.1574 -0.8379 0.5148 0.9834 148.433 -4.1413

300 0.2531 3.5586 3.5676 85.9315 -1.1312 0.6065 1.2835 151.803 1.2869 3.0351 3.2966 67.0224 -1.0438 0.6707 1.2407 147.279 -6.1286

305 0.3106 4.5025 4.5132 86.0537 -1.3878 0.8398 1.6221 148.821 1.5935 3.743 4.0681 66.9389 -1.2661 0.8538 1.5271 146.005 -8.6868

310 0.3898 5.6235 5.637 86.0347 -1.6687 1.1412 2.0216 145.634 1.9461 4.5573 4.9554 66.8757 -1.5106 1.0738 1.8534 144.594 -11.9687

315 0.5066 6.9937 7.012 85.8569 -1.9798 1.5345 2.5049 142.221 2.3661 5.5246 6.01 66.8151 -1.7874 1.3454 2.2371 143.031 -16.2052

320 0.6982 8.8151 8.8427 85.4713 -2.3564 2.0831 3.1452 138.522 2.9253 6.782 7.3859 66.6678 -2.1099 1.7188 2.7214 140.833 -21.9864

325 0.9866 11.1214 11.165 84.9303 -2.7651 2.8002 3.9353 134.638 3.6102 8.3455 9.0929 66.6071 -2.5174 2.1816 3.3312 139.087 -29.5214

330 1.4766 14.4539 14.529 84.1668 -3.2815 3.8506 5.0592 130.438 4.5956 10.5805 11.5354 66.5225 -3.0722 2.8549 4.1939 137.099 -40.4187

335 2.7612 21.9426 22.116 82.8279 -4.2362 6.23 7.5338 124.214 6.7645 15.544 16.9521 66.482 -4.2847 4.3535 6.1083 134.544 -64.1517

340 5.382 35.4553 35.861 81.3685 -5.7001 10.542 11.9843 118.4 10.6148 24.3202 26.5357 66.4207 -6.2511 7.0575 9.4278 131.532 -107.074

345 16.6362 85.11 86.721 78.94 -9.109 27.3592 28.8357 108.415 23.5034 54.2553 59.1274 66.5777 -12.08 16.5102 20.4575 126.192 -263.358

350 225.006 229.209 321.19 45.5302 217.476 213.788 304.961 44.5101 -113.033 -163.744 198.969 235.383 140.564 -16.51 141.53 353.301 -805.875

355 -5.4588 -42.941 43.286 262.755 9.3796 -10.136 13.8099 312.781 -17.0921 -35.6366 39.5235 244.377 9.6316 -10.51 14.2556 312.503 131.525

360 -3.7871 -19.925 20.282 259.238 2.9717 -4.994 5.8113 300.755 -7.4675 -15.6102 17.3044 244.435 3.5588 -4.9174 6.0701 305.894 60.5375

Appendix A5


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 1.6182 6.8397 7.0285 76.689 0.6744 -2.0015 2.1121 288.6198 1.0049 -1.5405 1.8393 303.1178

5 1.1499 4.3188 4.4693 75.0903 0.3365 -1.2037 1.2499 285.6181 0.6038 -1.0247 1.1894 300.511

10 0.9227 3.0892 3.2241 73.3693 0.1878 -0.818 0.8393 282.9296 0.4012 -0.7594 0.8589 297.8505

15 0.7743 2.3519 2.4761 71.7769 0.1088 -0.5793 0.5894 280.6392 0.3118 -0.5776 0.6564 298.3578

20 0.7046 1.9598 2.0826 70.2238 0.0683 -0.4438 0.4491 278.7508 0.2484 -0.4945 0.5534 296.6676

25 0.6801 1.7511 1.8786 68.7747 0.046 -0.3595 0.3624 277.2936 0.2125 -0.4529 0.5003 295.1366

30 0.6916 1.6648 1.8027 67.4392 0.0336 -0.306 0.3078 276.2689 0.1937 -0.4398 0.4806 293.7738

35 0.7323 1.662 1.8162 66.2207 0.0269 -0.2707 0.2721 275.6738 0.1858 -0.4462 0.4834 292.6003

40 0.8204 1.7589 1.9408 64.9952 0.0245 -0.2571 0.2583 275.437 0.1593 -0.4975 0.5224 287.7581

45 0.9009 1.8475 2.0555 64.0051 0.0235 -0.2369 0.2381 275.6738 0.1623 -0.5238 0.5484 287.2205

50 0.992 1.9572 2.1942 63.1205 0.0242 -0.2194 0.2207 276.2964 0.1684 -0.5531 0.5782 286.9305

55 1.0884 2.0759 2.3439 62.3326 0.0259 -0.2031 0.2048 277.2688 0.1764 -0.582 0.6082 286.8619

60 1.185 2.1947 2.4941 61.6332 0.0282 -0.1874 0.1895 278.5487 0.1859 -0.6082 0.6359 286.9948

65 1.2778 2.3067 2.637 61.0149 0.0306 -0.172 0.1747 280.0919 0.1963 -0.6299 0.6598 287.3131

70 1.3635 2.4071 2.7664 60.471 0.0329 -0.1568 0.1602 281.8562 0.2075 -0.6463 0.6788 287.802

75 1.4392 2.4923 2.8779 59.9955 0.0348 -0.1418 0.146 283.8031 0.2192 -0.6572 0.6928 288.447

80 1.4887 2.5033 2.9125 59.2592 0.0266 -0.0932 0.0969 285.9502 0.2302 -0.6645 0.7033 289.1034

85 1.5408 2.5481 2.9777 58.8382 0.0244 -0.0732 0.0772 288.3981 0.2428 -0.6669 0.7097 290.0055

90 1.5799 2.5752 3.0212 58.4705 0.0209 -0.0543 0.0582 291.0984 0.2554 -0.6646 0.712 291.024

95 1.6052 2.5843 3.0422 58.1539 0.0164 -0.0366 0.0401 294.1675 0.2679 -0.6582 0.7106 292.1449

100 1.6162 2.5752 3.0404 57.8868 0.0109 -0.0204 0.0232 298.0861 0.2797 -0.6479 0.7057 293.3544

105 1.6127 2.5479 3.0154 57.6683 0.0045 -0.0059 0.0075 307.277 0.2908 -0.634 0.6975 294.6389

110 1.5943 2.5024 2.9671 57.4979 -0.0025 0.0067 0.0072 110.5978 0.3006 -0.6167 0.6861 295.9845

115 1.5703 2.4405 2.902 57.2406 -0.0042 0.008 0.009 117.4645 0.2987 -0.5836 0.6556 297.1011

120 1.5226 2.3572 2.8062 57.1406 -0.01 0.0151 0.0181 123.652 0.3022 -0.5575 0.6341 298.4636

125 1.4589 2.2539 2.6848 57.0857 -0.0153 0.0199 0.0251 127.6524 0.3025 -0.5277 0.6082 299.8282

130 1.3783 2.1286 2.5359 57.0769 -0.0198 0.0225 0.03 131.2545 0.2988 -0.4939 0.5772 301.1724

135 1.2789 1.978 2.3555 57.1153 -0.0229 0.0231 0.0325 134.7889 0.2897 -0.4554 0.5397 302.4657

140 1.1573 1.7959 2.1365 57.2017 -0.0243 0.0216 0.0325 138.3781 0.2736 -0.4109 0.4937 303.6604

145 1.0069 1.5707 1.8658 57.3375 -0.0235 0.0183 0.0298 142.0394 0.2476 -0.3581 0.4353 304.6647

150 0.8144 1.2797 1.5169 57.5273 -0.0196 0.0135 0.0238 145.3919 0.2064 -0.2921 0.3576 305.2462

155 0.5492 0.8728 1.0312 57.8191 -0.0103 0.0075 0.0127 143.9331 0.1389 -0.2024 0.2455 304.4617

160 0.1277 0.2189 0.2534 59.7412 0.0138 0.0006 0.0138 2.4571 0.0168 -0.0611 0.0634 285.4042

165 -1.0267 -1.5653 1.8719 236.739 0.1219 0.0044 0.1219 2.0573 -0.3394 0.3173 0.4646 136.9219

170 -7.7244 -9.832 12.5033 231.8454 2.1766 0.0486 2.1772 1.2782 -2.014 2.2317 3.0061 132.0642

175 3.9146 11.5424 12.1882 71.2655 2.9195 -0.109 2.9215 357.8609 2.5058 -2.0821 3.2579 320.2762

180 2.3853 5.2172 5.7366 65.43 0.6042 -0.0634 0.6075 354.0065 1.1437 -1.0186 1.5315 318.3089

185 1.7374 3.7413 4.125 65.0907 0.3649 -0.0588 0.3696 350.8397 0.846 -0.7332 1.1195 319.084

190 1.388 3.0534 3.3541 65.5547 0.2983 -0.0611 0.3045 348.4255 0.706 -0.5995 0.9262 319.665

195 1.1496 2.6243 2.8651 66.3447 0.2753 -0.0649 0.2828 346.7355 0.6198 -0.5143 0.8054 320.3129

200 0.9677 2.3149 2.509 67.3133 0.2679 -0.0691 0.2767 345.5487 0.5575 -0.4523 0.7179 320.9488

205 0.8201 2.0706 2.2271 68.3928 0.2665 -0.073 0.2763 344.6721 0.5075 -0.4032 0.6482 321.5345

210 0.6959 1.8655 1.9911 69.5419 0.2663 -0.0765 0.2771 343.9677 0.4643 -0.3622 0.5888 322.0451

215 0.5526 1.5714 1.6657 70.6232 0.2455 -0.068 0.2548 344.5261 0.3965 -0.3085 0.5024 322.1167

220 0.4631 1.4132 1.4871 71.8551 0.2426 -0.0695 0.2524 344.0182 0.3601 -0.2777 0.4547 322.3655

225 0.3853 1.267 1.3243 73.085 0.2367 -0.0702 0.2469 343.4837 0.325 -0.2497 0.4099 322.468

230 0.3174 1.1293 1.1731 74.2998 0.2274 -0.07 0.238 342.8941 0.2905 -0.2238 0.3667 322.3909

235 0.2581 0.9971 1.03 75.4894 0.2146 -0.0688 0.2254 342.2325 0.2561 -0.1995 0.3246 322.0855

240 0.2061 0.8682 0.8923 76.6467 0.1983 -0.0664 0.2091 341.4884 0.2212 -0.1761 0.2828 321.4742

245 0.1606 0.7406 0.7578 77.7667 0.1784 -0.0626 0.189 340.6549 0.1856 -0.1534 0.2408 320.424

250 0.1208 0.6126 0.6244 78.8468 0.1548 -0.0572 0.165 339.7262 0.1489 -0.1309 0.1982 318.6815

255 0.086 0.4825 0.4901 79.8878 0.1276 -0.0497 0.1369 338.6955 0.1109 -0.1082 0.1549 315.6942

260 0.0559 0.3487 0.3532 80.8998 0.0966 -0.0399 0.1045 337.55 0.0713 -0.085 0.111 309.993

265 0.0339 0.236 0.2384 81.8367 0.0681 -0.0313 0.075 335.3284 0.0375 -0.0652 0.0752 299.892

270 0.0098 0.0821 0.0827 83.2194 0.0278 -0.0137 0.031 333.8382 -0.0077 -0.0386 0.0394 258.6633

275 -0.0172 -0.1158 0.117 261.5549 -0.0286 0.0144 0.032 153.2698 -0.0362 0.0194 0.041 151.8579

280 -0.0344 -0.2885 0.2905 263.1983 -0.0771 0.0415 0.0876 151.72 -0.0855 0.05 0.099 149.666

285 -0.0494 -0.4743 0.4769 264.0561 -0.1299 0.0746 0.1498 150.1293 -0.1369 0.0835 0.1604 148.6144

290 -0.0629 -0.6772 0.6801 264.6891 -0.1874 0.1152 0.22 148.4081 -0.1909 0.1207 0.2258 147.6885

295 -0.0762 -0.9018 0.905 265.1724 -0.2499 0.1652 0.2995 146.5345 -0.2479 0.1627 0.2965 146.7262

300 -0.0905 -1.1548 1.1583 265.519 -0.3179 0.2268 0.3906 144.4949 -0.3087 0.2108 0.3738 145.6749

305 -0.108 -1.4453 1.4494 265.725 -0.3923 0.3034 0.496 142.2792 -0.3745 0.267 0.46 144.5103

310 -0.1318 -1.7867 1.7916 265.78 -0.4741 0.3995 0.6199 139.8801 -0.4471 0.3342 0.5582 143.2188

315 -0.1665 -2.1995 2.2057 265.6702 -0.565 0.5215 0.7689 137.2938 -0.5295 0.4168 0.6739 141.7917

320 -0.223 -2.7423 2.7514 265.3521 -0.6761 0.6876 0.9643 134.5176 -0.6258 0.5299 0.82 139.7448

325 -0.3065 -3.4208 3.4345 264.88 -0.7974 0.8992 1.2019 131.5652 -0.7484 0.6692 1.0039 138.1956

330 -0.4454 -4.3866 4.4091 264.202 -0.9532 1.2007 1.5331 128.4447 -0.9164 0.8707 1.2641 136.4651

335 -0.7954 -6.5052 6.5536 263.0291 -1.2509 1.8557 2.2379 123.9827 -1.289 1.3142 1.8408 134.4456

340 -1.4388 -10.124 10.2257 261.9113 -1.7475 2.9299 3.4114 120.814 -1.9118 2.0959 2.8369 132.3697

345 -3.6299 -21.7675 22.0681 260.5327 -3.276 6.2709 7.075 117.5831 -3.9272 4.6636 6.0969 130.1008

350 19.9199 149.7112 151.0306 82.421 26.7641 -53.9511 60.2249 296.3851 22.9414 -26.1181 34.763 311.2952

355 3.2912 16.5228 16.8474 78.7345 2.0741 -5.0755 5.483 292.2277 2.5703 -3.5111 4.3514 306.2061

360 1.6182 6.8397 7.0285 76.689 0.6744 -2.0015 2.1121 288.6198 1.0049 -1.5405 1.8393 303.1178

Appendix A5


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 -1.6182 -6.8397 7.0285 256.689 0.6744 -2.0015 2.1121 288.62 -2.2934 -4.8388 5.3548 244.641 1.0049 -1.5405 1.8393 303.118 208.131

5 -1.1499 -4.3188 4.4693 255.09 0.3365 -1.2037 1.2499 285.618 -1.487 -3.1155 3.4522 244.485 0.6038 -1.0247 1.1894 300.511 127.871

10 -0.9227 -3.0892 3.2241 253.369 0.1878 -0.818 0.8393 282.93 -1.111 -2.2716 2.5288 243.938 0.4012 -0.7594 0.8589 297.851 87.7013

15 -0.7743 -2.3519 2.4761 251.777 0.1088 -0.5793 0.5894 280.639 -0.8836 -1.773 1.9809 243.51 0.3118 -0.5776 0.6564 298.358 63.0322

20 -0.7046 -1.9598 2.0826 250.224 0.0683 -0.4438 0.4491 278.751 -0.7733 -1.5163 1.7021 242.977 0.2484 -0.4945 0.5534 296.668 48.7059

25 -0.6801 -1.7511 1.8786 248.775 0.046 -0.3595 0.3624 277.294 -0.7265 -1.3919 1.5701 242.44 0.2125 -0.4529 0.5003 295.137 39.5478

30 -0.6916 -1.6648 1.8027 247.439 0.0336 -0.306 0.3078 276.269 -0.7256 -1.3591 1.5406 241.903 0.1937 -0.4398 0.4806 293.774 33.3486

35 -0.7323 -1.662 1.8162 246.221 0.0269 -0.2707 0.2721 275.674 -0.7595 -1.3915 1.5853 241.373 0.1858 -0.4462 0.4834 292.6 28.6465

40 -0.8204 -1.7589 1.9408 244.995 0.0245 -0.2571 0.2583 275.437 -0.8451 -1.502 1.7234 240.635 0.1593 -0.4975 0.5224 287.758 24.9547

45 -0.9009 -1.8475 2.0555 244.005 0.0235 -0.2369 0.2381 275.674 -0.9247 -1.6109 1.8574 240.142 0.1623 -0.5238 0.5484 287.221 20.3692

50 -0.992 -1.9572 2.1942 243.121 0.0242 -0.2194 0.2207 276.296 -1.0165 -1.738 2.0134 239.678 0.1684 -0.5531 0.5782 286.931 15.1569

55 -1.0884 -2.0759 2.3439 242.333 0.0259 -0.2031 0.2048 277.269 -1.1145 -1.8729 2.1795 239.245 0.1764 -0.582 0.6082 286.862 9.1031

60 -1.185 -2.1947 2.4941 241.633 0.0282 -0.1874 0.1895 278.549 -1.2134 -2.0074 2.3456 238.849 0.1859 -0.6082 0.6359 286.995 2.1632

65 -1.2778 -2.3067 2.637 241.015 0.0306 -0.172 0.1747 280.092 -1.3087 -2.1349 2.504 238.492 0.1963 -0.6299 0.6598 287.313 -5.5767

70 -1.3635 -2.4071 2.7664 240.471 0.0329 -0.1568 0.1602 281.856 -1.3966 -2.2504 2.6485 238.177 0.2075 -0.6463 0.6788 287.802 -13.936

75 -1.4392 -2.4923 2.8779 239.996 0.0348 -0.1418 0.146 283.803 -1.4742 -2.3506 2.7746 237.906 0.2192 -0.6572 0.6928 288.447 -22.6729

80 -1.4887 -2.5033 2.9125 239.259 0.0266 -0.0932 0.0969 285.95 -1.5155 -2.4102 2.8471 237.839 0.2302 -0.6645 0.7033 289.103 -31.3865

85 -1.5408 -2.5481 2.9777 238.838 0.0244 -0.0732 0.0772 288.398 -1.5653 -2.475 2.9284 237.688 0.2428 -0.6669 0.7097 290.006 -39.9517

90 -1.5799 -2.5752 3.0212 238.471 0.0209 -0.0543 0.0582 291.098 -1.601 -2.521 2.9864 237.583 0.2554 -0.6646 0.712 291.024 -48.0767

95 -1.6052 -2.5843 3.0422 238.154 0.0164 -0.0366 0.0401 294.168 -1.6217 -2.5477 3.0201 237.522 0.2679 -0.6582 0.7106 292.145 -55.5144

100 -1.6162 -2.5752 3.0404 237.887 0.0109 -0.0204 0.0232 298.086 -1.6272 -2.5548 3.029 237.506 0.2797 -0.6479 0.7057 293.354 -62.0426

105 -1.6127 -2.5479 3.0154 237.668 0.0045 -0.0059 0.0075 307.277 -1.6173 -2.542 3.0129 237.535 0.2908 -0.634 0.6975 294.639 -67.469

110 -1.5943 -2.5024 2.9671 237.498 -0.0025 0.0067 0.0072 110.598 -1.5919 -2.5092 2.9715 237.608 0.3006 -0.6167 0.6861 295.985 -71.6337

115 -1.5703 -2.4405 2.902 237.241 -0.0042 0.008 0.009 117.465 -1.5662 -2.4485 2.9066 237.395 0.2987 -0.5836 0.6556 297.101 -74.6932

120 -1.5226 -2.3572 2.8062 237.141 -0.01 0.0151 0.0181 123.652 -1.5126 -2.3722 2.8134 237.478 0.3022 -0.5575 0.6341 298.464 -75.9889

125 -1.4589 -2.2539 2.6848 237.086 -0.0153 0.0199 0.0251 127.652 -1.4435 -2.2737 2.6933 237.59 0.3025 -0.5277 0.6082 299.828 -75.7042

130 -1.3783 -2.1286 2.5359 237.077 -0.0198 0.0225 0.03 131.255 -1.3585 -2.1511 2.5442 237.726 0.2988 -0.4939 0.5772 301.172 -73.7649

135 -1.2789 -1.978 2.3555 237.115 -0.0229 0.0231 0.0325 134.789 -1.256 -2.001 2.3626 237.885 0.2897 -0.4554 0.5397 302.466 -70.0805

140 -1.1573 -1.7959 2.1365 237.202 -0.0243 0.0216 0.0325 138.378 -1.1329 -1.8174 2.1416 238.062 0.2736 -0.4109 0.4937 303.66 -64.501

145 -1.0069 -1.5707 1.8658 237.338 -0.0235 0.0183 0.0298 142.039 -0.9833 -1.589 1.8686 238.249 0.2476 -0.3581 0.4353 304.665 -56.7279

150 -0.8144 -1.2797 1.5169 237.527 -0.0196 0.0135 0.0238 145.392 -0.7947 -1.2932 1.5178 238.428 0.2064 -0.2921 0.3576 305.246 -46.1149

155 -0.5492 -0.8728 1.0312 237.819 -0.0103 0.0075 0.0127 143.933 -0.5389 -0.8803 1.0322 238.524 0.1389 -0.2024 0.2455 304.462 -31.1347

160 -0.1277 -0.2189 0.2534 239.741 0.0138 0.0006 0.0138 2.4571 -0.1418 -0.2198 0.2616 237.166 0.0168 -0.0611 0.0634 285.404 -7.5889

165 1.0267 1.5653 1.8719 56.739 0.1219 0.0044 0.1219 2.0573 0.9016 1.5583 1.8003 59.9472 -0.3394 0.3173 0.4646 136.922 54.0936

170 7.7244 9.832 12.503 51.8454 2.1766 0.0486 2.1772 1.2782 5.4948 9.7404 11.1834 60.5717 -2.014 2.2317 3.0061 132.064 335.458

175 -3.9146 -11.542 12.188 251.266 2.9195 -0.109 2.9215 357.861 -6.8944 -11.4823 13.3931 239.018 2.5058 -2.0821 3.2579 320.276 -360.281

180 -2.3853 -5.2172 5.7366 245.43 0.6042 -0.0634 0.6075 354.007 -2.9996 -5.1619 5.9701 239.839 1.1437 -1.0186 1.5315 318.309 -158.758

185 -1.7374 -3.7413 4.125 245.091 0.3649 -0.0588 0.3696 350.84 -2.1071 -3.6863 4.2461 240.248 0.846 -0.7332 1.1195 319.084 -108.806

190 -1.388 -3.0534 3.3541 245.555 0.2983 -0.0611 0.3045 348.426 -1.6894 -2.9948 3.4385 240.573 0.706 -0.5995 0.9262 319.665 -84.1686

195 -1.1496 -2.6243 2.8651 246.345 0.2753 -0.0649 0.2828 346.736 -1.4271 -2.5613 2.932 240.874 0.6198 -0.5143 0.8054 320.313 -68.0832

200 -0.9677 -2.3149 2.509 247.313 0.2679 -0.0691 0.2767 345.549 -1.2374 -2.2473 2.5654 241.161 0.5575 -0.4523 0.7179 320.949 -56.1222

205 -0.8201 -2.0706 2.2271 248.393 0.2665 -0.073 0.2763 344.672 -1.088 -1.9987 2.2757 241.438 0.5075 -0.4032 0.6482 321.535 -46.5579

210 -0.6959 -1.8655 1.9911 249.542 0.2663 -0.0765 0.2771 343.968 -0.9634 -1.7899 2.0327 241.708 0.4643 -0.3622 0.5888 322.045 -38.5726

215 -0.5526 -1.5714 1.6657 250.623 0.2455 -0.068 0.2548 344.526 -0.7991 -1.5041 1.7032 242.02 0.3965 -0.3085 0.5024 322.117 -29.5232

220 -0.4631 -1.4132 1.4871 251.855 0.2426 -0.0695 0.2524 344.018 -0.7065 -1.3443 1.5186 242.275 0.3601 -0.2777 0.4547 322.366 -23.8831

225 -0.3853 -1.267 1.3243 253.085 0.2367 -0.0702 0.2469 343.484 -0.6226 -1.1973 1.3496 242.525 0.325 -0.2497 0.4099 322.468 -18.9722

230 -0.3174 -1.1293 1.1731 254.3 0.2274 -0.07 0.238 342.894 -0.5454 -1.0597 1.1918 242.768 0.2905 -0.2238 0.3667 322.391 -14.6895

235 -0.2581 -0.9971 1.03 255.489 0.2146 -0.0688 0.2254 342.233 -0.4731 -0.9287 1.0422 243.003 0.2561 -0.1995 0.3246 322.086 -10.9708

240 -0.2061 -0.8682 0.8923 256.647 0.1983 -0.0664 0.2091 341.488 -0.4047 -0.802 0.8984 243.226 0.2212 -0.1761 0.2828 321.474 -7.7786

245 -0.1606 -0.7406 0.7578 257.767 0.1784 -0.0626 0.189 340.655 -0.3392 -0.6782 0.7582 243.429 0.1856 -0.1534 0.2408 320.424 -5.0958

250 -0.1208 -0.6126 0.6244 258.847 0.1548 -0.0572 0.165 339.726 -0.2757 -0.5555 0.6202 243.603 0.1489 -0.1309 0.1982 318.682 -2.9219

255 -0.086 -0.4825 0.4901 259.888 0.1276 -0.0497 0.1369 338.696 -0.2137 -0.4328 0.4827 243.72 0.1109 -0.1082 0.1549 315.694 -1.2707

260 -0.0559 -0.3487 0.3532 260.9 0.0966 -0.0399 0.1045 337.55 -0.1525 -0.3089 0.3445 243.72 0.0713 -0.085 0.111 309.993 -0.1688

265 -0.0339 -0.236 0.2384 261.837 0.0681 -0.0313 0.075 335.328 -0.102 -0.2047 0.2287 243.51 0.0375 -0.0652 0.0752 299.892 0.4003

270 -0.0098 -0.0821 0.0827 263.219 0.0278 -0.0137 0.031 333.838 -0.0376 -0.0685 0.0781 241.236 -0.0077 -0.0386 0.0394 258.663 0.2972

275 0.0172 0.1158 0.117 81.5549 -0.0286 0.0144 0.032 153.27 0.0458 0.1014 0.1113 65.6717 -0.0362 0.0194 0.041 151.858 -0.8282

280 0.0344 0.2885 0.2905 83.1983 -0.0771 0.0415 0.0876 151.72 0.1116 0.247 0.271 65.6948 -0.0855 0.05 0.099 149.666 -2.5553

285 0.0494 0.4743 0.4769 84.0561 -0.1299 0.0746 0.1498 150.129 0.1794 0.3998 0.4382 65.8356 -0.1369 0.0835 0.1604 148.614 -5.1875

290 0.0629 0.6772 0.6801 84.6891 -0.1874 0.1152 0.22 148.408 0.2504 0.562 0.6153 65.9838 -0.1909 0.1207 0.2258 147.689 -8.8477

295 0.0762 0.9018 0.905 85.1724 -0.2499 0.1652 0.2995 146.535 0.3261 0.7367 0.8057 66.1209 -0.2479 0.1627 0.2965 146.726 -13.6977

300 0.0905 1.1548 1.1583 85.519 -0.3179 0.2268 0.3906 144.495 0.4086 0.9281 1.014 66.2394 -0.3087 0.2108 0.3738 145.675 -19.9551

305 0.108 1.4453 1.4494 85.725 -0.3923 0.3034 0.496 142.279 0.5005 1.142 1.2469 66.3347 -0.3745 0.267 0.46 144.51 -27.9197

310 0.1318 1.7867 1.7916 85.78 -0.4741 0.3995 0.6199 139.88 0.6061 1.3874 1.514 66.4027 -0.4471 0.3342 0.5582 143.219 -38.0216

315 0.1665 2.1995 2.2057 85.6702 -0.565 0.5215 0.7689 137.294 0.7318 1.6781 1.8307 66.4398 -0.5295 0.4168 0.6739 141.792 -50.9094

320 0.223 2.7423 2.7514 85.3521 -0.6761 0.6876 0.9643 134.518 0.8992 2.0549 2.2431 66.366 -0.6258 0.5299 0.82 139.745 -68.2866

325 0.3065 3.4208 3.4345 84.88 -0.7974 0.8992 1.2019 131.565 1.1042 2.5217 2.7529 66.3536 -0.7484 0.6692 1.0039 138.196 -90.6186

330 0.4454 4.3866 4.4091 84.202 -0.9532 1.2007 1.5331 128.445 1.3989 3.1861 3.4796 66.295 -0.9164 0.8707 1.2641 136.465 -122.377

335 0.7954 6.5052 6.5536 83.0291 -1.2509 1.8557 2.2379 123.983 2.0466 4.6498 5.0802 66.2431 -1.289 1.3142 1.8408 134.446 -189.635

340 1.4388 10.124 10.226 81.9113 -1.7475 2.9299 3.4114 120.814 3.1867 7.1944 7.8686 66.1095 -1.9118 2.0959 2.8369 132.37 -304.468

345 3.6299 21.7675 22.068 80.5327 -3.276 6.2709 7.075 117.583 6.9057 15.4965 16.9655 65.9808 -3.9272 4.6636 6.0969 130.101 -668.403

350 -19.92 -149.71 151.03 262.421 26.7641 -53.951 60.2249 296.385 -46.7695 -95.829 106.633 243.985 22.9414 -26.118 34.763 311.295 4591.8

355 -3.2912 -16.523 16.847 258.735 2.0741 -5.0755 5.483 292.228 -5.3676 -11.4491 12.6449 244.882 2.5703 -3.5111 4.3514 306.206 509.605

360 -1.6182 -6.8397 7.0285 256.689 0.6744 -2.0015 2.1121 288.62 -2.2934 -4.8388 5.3548 244.641 1.0049 -1.5405 1.8393 303.118 208.131

Appendix A6


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 -0.0606 3.9848 3.9853 90.8709 1.552 -1.974 2.511 308.1744 1.552 -1.974 2.511 308.1744

5 0.0726 2.7416 2.7425 88.484 0.7634 -1.1167 1.3527 304.3588 0.7634 -1.1167 1.3527 304.3588

10 0.0724 1.9916 1.9929 87.9179 0.4564 -0.7166 0.8496 302.4918 0.4564 -0.7166 0.8496 302.4918

15 0.0298 1.4781 1.4784 88.8451 0.3088 -0.4779 0.569 302.8729 0.3088 -0.4779 0.569 302.8729

20 0.0155 1.2045 1.2046 89.2643 0.2359 -0.3501 0.4222 303.973 0.2359 -0.3501 0.4222 303.973

25 0.0229 1.0648 1.065 88.7694 0.1981 -0.279 0.3422 305.367 0.1981 -0.279 0.3422 305.367

30 0.0553 1.0217 1.0232 86.9027 0.1786 -0.2428 0.3014 306.3397 0.1786 -0.2428 0.3014 306.3397

35 0.1119 1.048 1.054 83.9052 0.1694 -0.2273 0.2835 306.6953 0.1694 -0.2273 0.2835 306.6953

40 0.2142 1.1659 1.1854 79.5913 0.1671 -0.2345 0.288 305.4765 0.1671 -0.2345 0.288 305.4765

45 0.3087 1.2704 1.3074 76.34 0.1682 -0.235 0.289 305.582 0.1682 -0.235 0.289 305.582

50 0.4146 1.3926 1.453 73.4221 0.1721 -0.2373 0.2931 305.9595 0.1721 -0.2373 0.2931 305.9595

55 0.5266 1.5219 1.6105 70.9127 0.1783 -0.2392 0.2983 306.6974 0.1783 -0.2392 0.2983 306.6974

60 0.6403 1.65 1.7699 68.7908 0.1859 -0.2397 0.3033 307.7921 0.1859 -0.2397 0.3033 307.7921

65 0.7516 1.7709 1.9238 67.0015 0.1943 -0.2382 0.3074 309.1951 0.1943 -0.2382 0.3074 309.1951

70 0.8573 1.8799 2.0662 65.4862 0.2029 -0.2347 0.3103 310.8443 0.2029 -0.2347 0.3103 310.8443

75 0.9547 1.9743 2.193 64.1928 0.2112 -0.2291 0.3116 312.6813 0.2112 -0.2291 0.3116 312.6813

80 1.0278 2.0023 2.2507 62.8292 0.2085 -0.1924 0.2837 317.3062 0.2085 -0.1924 0.2837 317.3062

85 1.1045 2.0587 2.3362 61.7861 0.2123 -0.178 0.277 320.0179 0.2123 -0.178 0.277 320.0179

90 1.1698 2.0984 2.4025 60.8609 0.2142 -0.1624 0.2689 322.8298 0.2142 -0.1624 0.2689 322.8298

95 1.2232 2.1215 2.4488 60.0339 0.2141 -0.146 0.2592 325.7082 0.2141 -0.146 0.2592 325.7082

100 1.2639 2.1278 2.4749 59.2896 0.2118 -0.1291 0.248 328.6303 0.2118 -0.1291 0.248 328.6303

105 1.2918 2.1176 2.4805 58.6154 0.2069 -0.112 0.2353 331.5855 0.2069 -0.112 0.2353 331.5855

110 1.3064 2.0907 2.4653 58.0009 0.1996 -0.0949 0.221 334.5753 0.1996 -0.0949 0.221 334.5753

115 1.3165 2.0495 2.4359 57.2845 0.1953 -0.0871 0.2138 335.9564 0.1953 -0.0871 0.2138 335.9564

120 1.3039 1.988 2.3774 56.7385 0.1846 -0.0725 0.1983 338.5505 0.1846 -0.0725 0.1983 338.5505

125 1.2758 1.9077 2.295 56.2264 0.1719 -0.0588 0.1817 341.1108 0.1719 -0.0588 0.1817 341.1108

130 1.2302 1.8063 2.1854 55.743 0.1574 -0.0461 0.164 343.6745 0.1574 -0.0461 0.164 343.6745

135 1.1635 1.6794 2.0431 55.2853 0.1414 -0.0344 0.1455 346.3246 0.1414 -0.0344 0.1455 346.3246

140 1.0695 1.5192 1.8579 54.856 0.1247 -0.0237 0.1269 349.2379 0.1247 -0.0237 0.1269 349.2379

145 0.9354 1.3105 1.6101 54.4807 0.1088 -0.0138 0.1097 352.7752 0.1088 -0.0138 0.1097 352.7752

150 0.7344 1.0219 1.2585 54.2962 0.0978 -0.0043 0.0978 357.4921 0.0978 -0.0043 0.0978 357.4921

155 0.3994 0.5798 0.7041 55.4403 0.1043 0.0055 0.1045 3.021 0.1043 0.0055 0.1045 3.021

160 -0.2802 -0.2307 0.3629 219.4651 0.1805 0.0163 0.1812 5.1555 0.1805 0.0163 0.1812 5.1555

165 -2.9789 -3.0602 4.2707 225.7717 0.8217 0.0394 0.8227 2.7476 0.8217 0.0394 0.8227 2.7476

170 -32.3779 -27.0749 42.2064 219.9029 12.8531 -0.337 12.8575 358.4982 12.8531 -0.337 12.8575 358.4982

175 -18.455 -4.6575 19.0336 194.1641 15.4368 -1.1567 15.48 355.7148 15.4368 -1.1567 15.48 355.7148

180 -0.6003 2.84 2.9028 101.9353 2.7892 -0.2906 2.8043 354.0522 2.7892 -0.2906 2.8043 354.0522

185 0.6154 2.7285 2.797 77.2909 1.4519 -0.1788 1.4628 352.9785 1.4519 -0.1788 1.4628 352.9785

190 0.8401 2.4784 2.6169 71.2756 1.0206 -0.1409 1.0302 352.1371 1.0206 -0.1409 1.0302 352.1371

195 0.8614 2.261 2.4195 69.1439 0.821 -0.124 0.8303 351.414 0.821 -0.124 0.8303 351.414

200 0.8213 2.0786 2.235 68.4405 0.71 -0.1156 0.7193 350.749 0.71 -0.1156 0.7193 350.749

205 0.7591 1.9213 2.0659 68.4411 0.6399 -0.1115 0.6496 350.1138 0.6399 -0.1115 0.6496 350.1138

210 0.6891 1.7812 1.9099 68.8486 0.5906 -0.1096 0.6007 349.4912 0.5906 -0.1096 0.6007 349.4912

215 0.6266 1.5847 1.7041 68.4268 0.4978 -0.0942 0.5066 349.2838 0.4978 -0.0942 0.5066 349.2838

220 0.5545 1.4663 1.5676 69.286 0.4684 -0.0936 0.4777 348.6961 0.4684 -0.0936 0.4777 348.6961

225 0.486 1.354 1.4386 70.2556 0.4405 -0.093 0.4502 348.0749 0.4405 -0.093 0.4502 348.0749

230 0.4219 1.246 1.3155 71.2932 0.412 -0.0922 0.4222 347.3926 0.412 -0.0922 0.4222 347.3926

235 0.3627 1.1408 1.197 72.3643 0.3818 -0.0908 0.3925 346.6184 0.3818 -0.0908 0.3925 346.6184

240 0.3084 1.0373 1.0822 73.4397 0.3492 -0.0889 0.3604 345.7139 0.3492 -0.0889 0.3604 345.7139

245 0.2593 0.9345 0.9698 74.4938 0.3138 -0.0863 0.3254 344.6282 0.3138 -0.0863 0.3254 344.6282

250 0.215 0.8314 0.8587 75.5026 0.2754 -0.0827 0.2875 343.2859 0.2754 -0.0827 0.2875 343.2859

255 0.1753 0.7269 0.7478 76.4417 0.234 -0.078 0.2466 341.564 0.234 -0.078 0.2466 341.564

260 0.1399 0.62 0.6356 77.2826 0.1896 -0.0719 0.2028 339.2321 0.1896 -0.0719 0.2028 339.2321

265 0.1087 0.5284 0.5395 78.373 0.1508 -0.0692 0.1659 335.3503 0.1508 -0.0692 0.1659 335.3503

270 0.0805 0.4068 0.4147 78.7993 0.0982 -0.0577 0.1139 329.5478 0.0982 -0.0577 0.1139 329.5478

275 0.0487 0.2416 0.2465 78.6041 0.0313 -0.0372 0.0486 310.0854 0.0313 -0.0372 0.0486 310.0854

280 0.0258 0.1018 0.105 75.7951 -0.0258 -0.019 0.032 216.4342 -0.0258 -0.019 0.032 216.4342

285 0.0043 -0.0517 0.0519 274.7081 -0.0853 0.0038 0.0854 177.4465 -0.0853 0.0038 0.0854 177.4465

290 -0.0166 -0.2235 0.2241 265.7446 -0.1474 0.0328 0.151 167.4639 -0.1474 0.0328 0.151 167.4639

295 -0.0379 -0.4194 0.4211 264.8404 -0.2126 0.0698 0.2238 161.8208 -0.2126 0.0698 0.2238 161.8208

300 -0.0608 -0.6475 0.6504 264.6318 -0.2813 0.1174 0.3048 157.3384 -0.2813 0.1174 0.3048 157.3384

305 -0.0876 -0.9187 0.9228 264.5557 -0.3538 0.1789 0.3964 153.1711 -0.3538 0.1789 0.3964 153.1711

310 -0.1211 -1.2485 1.2544 264.459 -0.4304 0.2586 0.5021 148.9949 -0.4304 0.2586 0.5021 148.9949

315 -0.1666 -1.661 1.6694 264.2711 -0.5113 0.3627 0.6269 144.6481 -0.5113 0.3627 0.6269 144.6481

320 -0.2363 -2.2206 2.2332 263.9262 -0.6034 0.5074 0.7884 139.9395 -0.6034 0.5074 0.7884 139.9395

325 -0.3401 -2.9473 2.9668 263.4182 -0.6895 0.6915 0.9766 134.917 -0.6895 0.6915 0.9766 134.917

330 -0.5182 -4.0252 4.0584 262.6639 -0.7733 0.95 1.225 129.1466 -0.7733 0.95 1.225 129.1466

335 -1.0121 -6.5479 6.6257 261.2132 -0.8198 1.4703 1.6834 119.1427 -0.8198 1.4703 1.6834 119.1427

340 -2.1784 -11.5154 11.7197 259.2876 -0.5933 2.2435 2.3206 104.8128 -0.5933 2.2435 2.3206 104.8128

345 -8.5169 -33.191 34.2663 255.6082 2.7045 3.9005 4.7464 55.2635 2.7045 3.9005 4.7464 55.2635

350 -275.5153 -524.5431 592.4982 242.2894 309.2266 -126.9339 334.2653 337.6824 309.2266 -126.9339 334.2653 337.6824

355 -2.2628 5.1018 5.5811 113.9186 6.2147 -5.6817 8.4204 317.5651 6.2147 -5.6817 8.4204 317.5651

360 -0.0606 3.9848 3.9853 90.8709 1.552 -1.974 2.511 308.1744 1.552 -1.974 2.511 308.1744

Appendix A6


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 1.3073 -0.3779 1.3608 343.876 -1.9873 -4.1323 4.5853 244.316 -1.9873 -4.1323 4.5853 244.316 1.3118 -1.0902 1.7057 320.27 121.257

5 0.7026 -0.3038 0.7655 336.616 -1.2848 -2.7119 3.0009 244.65 -1.2848 -2.7119 3.0009 244.65 0.7904 -0.7406 1.0831 316.863 82.9164

10 0.4577 -0.1974 0.4984 336.667 -0.9453 -1.9854 2.199 244.541 -0.9453 -1.9854 2.199 244.541 0.5438 -0.5429 0.7684 315.05 59.3002

15 0.3389 -0.0979 0.3527 343.878 -0.7318 -1.5413 1.7062 244.601 -0.7318 -1.5413 1.7062 244.601 0.4351 -0.393 0.5863 317.908 43.2102

20 0.2824 -0.0447 0.2859 351.006 -0.6261 -1.3126 1.4543 244.501 -0.6261 -1.3126 1.4543 244.501 0.3629 -0.3271 0.4886 317.97 34.2827

25 0.2554 -0.0159 0.2559 356.431 -0.5793 -1.2038 1.3359 244.3 -0.5793 -1.2038 1.3359 244.3 0.3232 -0.296 0.4383 317.513 29.0713

30 0.2439 -0.0042 0.2439 359.014 -0.5767 -1.18 1.3134 243.954 -0.5767 -1.18 1.3134 243.954 0.3028 -0.2904 0.4196 316.196 26.0832

35 0.2406 -0.0027 0.2406 359.358 -0.6083 -1.2183 1.3617 243.466 -0.6083 -1.2183 1.3617 243.466 0.2941 -0.3034 0.4226 314.113 24.1711

40 0.2429 -0.0175 0.2436 355.882 -0.6918 -1.333 1.5019 242.573 -0.6918 -1.333 1.5019 242.573 0.2671 -0.361 0.449 306.5 22.9882

45 0.2474 -0.0216 0.2484 355.003 -0.7698 -1.4456 1.6378 241.963 -0.7698 -1.4456 1.6378 241.963 0.2691 -0.3937 0.4769 304.357 20.6919

50 0.2539 -0.0252 0.2551 354.333 -0.8608 -1.5761 1.7959 241.359 -0.8608 -1.5761 1.7959 241.359 0.2736 -0.4297 0.5094 302.489 17.5759

55 0.2615 -0.0272 0.2629 354.065 -0.9588 -1.7146 1.9645 240.786 -0.9588 -1.7146 1.9645 240.786 0.2795 -0.4655 0.5429 300.985 13.4362

60 0.2697 -0.0273 0.2711 354.216 -1.0586 -1.8528 2.1339 240.259 -1.0586 -1.8528 2.1339 240.259 0.2862 -0.4986 0.5749 299.863 8.2311

65 0.2779 -0.0257 0.2791 354.719 -1.1555 -1.9841 2.2961 239.785 -1.1555 -1.9841 2.2961 239.785 0.2935 -0.5272 0.6034 299.103 2.0446

70 0.2856 -0.0225 0.2865 355.488 -1.2458 -2.1038 2.445 239.368 -1.2458 -2.1038 2.445 239.368 0.301 -0.5505 0.6274 298.669 -4.9481

75 0.2923 -0.0182 0.2929 356.444 -1.3264 -2.2083 2.576 239.008 -1.3264 -2.2083 2.576 239.008 0.3086 -0.5679 0.6464 298.517 -12.5125

80 0.2892 0.0138 0.2896 2.7348 -1.3719 -2.2719 2.654 238.874 -1.3719 -2.2719 2.654 238.874 0.3147 -0.5809 0.6607 298.451 -20.2194

85 0.2905 0.0246 0.2915 4.8412 -1.4261 -2.3413 2.7414 238.655 -1.4261 -2.3413 2.7414 238.655 0.3228 -0.5891 0.6717 298.717 -28.022

90 0.2895 0.0354 0.2917 6.9682 -1.4666 -2.3923 2.806 238.49 -1.4666 -2.3923 2.806 238.49 0.3306 -0.5926 0.6786 299.159 -35.5985

95 0.2861 0.0457 0.2897 9.0855 -1.4928 -2.4242 2.847 238.376 -1.4928 -2.4242 2.847 238.376 0.3381 -0.5916 0.6814 299.749 -42.7055

100 0.2801 0.0553 0.2855 11.1771 -1.5042 -2.4368 2.8637 238.314 -1.5042 -2.4368 2.8637 238.314 0.345 -0.5865 0.6805 300.461 -49.1208

105 0.2716 0.0639 0.2791 13.2378 -1.5006 -2.4299 2.8559 238.302 -1.5006 -2.4299 2.8559 238.302 0.3509 -0.5777 0.6759 301.274 -54.6474

110 0.2608 0.0712 0.2703 15.2693 -1.482 -2.4032 2.8235 238.339 -1.482 -2.4032 2.8235 238.339 0.3556 -0.5653 0.6678 302.169 -59.1155

115 0.2533 0.0681 0.2623 15.0404 -1.4631 -2.3499 2.7682 238.093 -1.4631 -2.3499 2.7682 238.093 0.349 -0.5377 0.641 302.985 -62.6646

120 0.2402 0.0708 0.2504 16.4319 -1.4168 -2.2805 2.6847 238.149 -1.4168 -2.2805 2.6847 238.149 0.3477 -0.516 0.6222 303.972 -64.6095

125 0.2261 0.072 0.2372 17.6596 -1.3551 -2.1889 2.5744 238.24 -1.3551 -2.1889 2.5744 238.24 0.3434 -0.4903 0.5986 305.006 -65.0983

130 0.2118 0.0717 0.2236 18.701 -1.2772 -2.0733 2.4351 238.366 -1.2772 -2.0733 2.4351 238.366 0.3354 -0.4601 0.5694 306.091 -64.0068

135 0.1985 0.0705 0.2106 19.54 -1.1812 -1.9298 2.2626 238.529 -1.1812 -1.9298 2.2626 238.529 0.323 -0.4246 0.5335 307.261 -61.1723

140 0.1881 0.0692 0.2004 20.1911 -1.0634 -1.7518 2.0492 238.742 -1.0634 -1.7518 2.0492 238.742 0.3048 -0.3818 0.4885 308.603 -56.3326

145 0.1838 0.0697 0.1965 20.7599 -0.916 -1.5264 1.7802 239.031 -0.916 -1.5264 1.7802 239.031 0.2792 -0.3282 0.4309 310.383 -48.9933

150 0.1926 0.076 0.2071 21.5367 -0.7232 -1.2276 1.4248 239.499 -0.7232 -1.2276 1.4248 239.499 0.2435 -0.2566 0.3537 313.502 -38.1055

155 0.2329 0.0988 0.253 22.9961 -0.4472 -0.7959 0.9129 240.671 -0.4472 -0.7959 0.9129 240.671 0.1939 -0.1491 0.2446 322.429 -21.1281

160 0.3662 0.1732 0.4051 25.3111 0.0199 -0.0644 0.0674 287.168 0.0199 -0.0644 0.0674 287.168 0.1268 0.0471 0.1353 20.3689 9.5125

165 1.1034 0.6292 1.2702 29.6909 1.4738 2.1571 2.6125 55.658 1.4738 2.1571 2.6125 55.658 0.0815 0.7305 0.735 83.6308 113.411

170 11.8853 6.7463 13.667 29.5802 12.0955 17.2202 21.0437 54.9157 12.0955 17.2202 21.0437 54.9157 2.8793 7.1143 7.6748 67.9658 982.46

175 10.8929 5.4336 12.173 26.5107 -0.8813 -4.1415 4.2342 257.987 -0.8813 -4.1415 4.2342 257.987 6.9108 2.3829 7.31 19.0245 190.134

180 1.6475 0.6438 1.7688 21.3436 -2.1465 -4.0426 4.5771 242.033 -2.1465 -4.0426 4.5771 242.033 1.7617 -0.383 1.8029 347.735 -86.4211

185 0.7642 0.2034 0.7908 14.902 -1.7526 -3.1855 3.6358 241.182 -1.7526 -3.1855 3.6358 241.182 1.103 -0.4657 1.1973 337.112 -81.0806

190 0.5011 0.0681 0.5057 7.7389 -1.4908 -2.6894 3.075 241 -1.4908 -2.6894 3.075 241 0.853 -0.4449 0.962 332.455 -69.8336

195 0.3887 0.0053 0.3887 0.7801 -1.3018 -2.3478 2.6845 240.993 -1.3018 -2.3478 2.6845 240.993 0.7171 -0.4113 0.8267 330.162 -59.6736

200 0.3321 -0.0306 0.3335 354.728 -1.155 -2.087 2.3853 241.04 -1.155 -2.087 2.3853 241.04 0.6273 -0.3782 0.7325 328.912 -50.8899

205 0.3008 -0.0536 0.3056 349.905 -1.0344 -1.8738 2.1403 241.101 -1.0344 -1.8738 2.1403 241.101 0.5599 -0.3476 0.6591 328.164 -43.226

210 0.282 -0.0689 0.2903 346.272 -0.9311 -1.6907 1.9302 241.157 -0.9311 -1.6907 1.9302 241.157 0.5048 -0.3196 0.5975 327.657 -36.4552

215 0.2288 -0.0875 0.245 339.084 -0.7922 -1.4407 1.6441 241.194 -0.7922 -1.4407 1.6441 241.194 0.4214 -0.2835 0.5079 326.066 -28.5657

220 0.2201 -0.0931 0.239 337.066 -0.7123 -1.2958 1.4787 241.204 -0.7123 -1.2958 1.4787 241.204 0.3791 -0.2596 0.4595 325.597 -23.3347

225 0.2111 -0.0963 0.232 335.489 -0.6392 -1.1618 1.326 241.18 -0.6392 -1.1618 1.326 241.18 0.3394 -0.2373 0.4141 325.031 -18.6773

230 0.2003 -0.0975 0.2228 334.035 -0.5714 -1.0355 1.1827 241.112 -0.5714 -1.0355 1.1827 241.112 0.301 -0.2164 0.3707 324.285 -14.5364

235 0.1867 -0.0976 0.2107 332.396 -0.5075 -0.9149 1.0463 240.984 -0.5075 -0.9149 1.0463 240.984 0.2633 -0.1965 0.3285 323.259 -10.8712

240 0.1695 -0.097 0.1953 330.229 -0.4466 -0.7981 0.9146 240.772 -0.4466 -0.7981 0.9146 240.772 0.2254 -0.1773 0.2868 321.809 -7.6537

245 0.1483 -0.096 0.1766 327.08 -0.3878 -0.6837 0.786 240.436 -0.3878 -0.6837 0.786 240.436 0.1871 -0.1586 0.2453 319.703 -4.8674

250 0.1227 -0.095 0.1552 322.25 -0.3305 -0.5702 0.6591 239.906 -0.3305 -0.5702 0.6591 239.906 0.1477 -0.1401 0.2036 316.525 -2.5056

255 0.0926 -0.0941 0.132 314.533 -0.2739 -0.4566 0.5324 239.04 -0.2739 -0.4566 0.5324 239.04 0.1071 -0.1214 0.1619 311.427 -0.5725

260 0.0578 -0.0932 0.1097 301.815 -0.2175 -0.3415 0.4049 237.51 -0.2175 -0.3415 0.4049 237.51 0.0649 -0.1022 0.1211 302.425 0.9169

265 0.0265 -0.0932 0.0969 285.908 -0.1706 -0.2442 0.2979 235.063 -0.1706 -0.2442 0.2979 235.063 0.0292 -0.0856 0.0905 288.836 1.8946

270 -0.0198 -0.0912 0.0934 257.743 -0.1099 -0.1174 0.1608 226.877 -0.1099 -0.1174 0.1608 226.877 -0.019 -0.0637 0.0664 253.406 2.4511

275 -0.0825 -0.0811 0.1157 224.517 -0.0296 0.0433 0.0525 124.341 -0.0296 0.0433 0.0525 124.341 -0.0504 -0.0104 0.0514 191.653 2.1172

280 -0.1373 -0.0741 0.156 208.335 0.0337 0.1802 0.1833 79.4032 0.0337 0.1802 0.1833 79.4032 -0.1026 0.0155 0.1038 171.404 1.3104

285 -0.1964 -0.0625 0.2061 197.646 0.0998 0.3246 0.3396 72.9146 0.0998 0.3246 0.3396 72.9146 -0.157 0.0442 0.1631 164.259 -0.282

290 -0.26 -0.0444 0.2637 189.695 0.1697 0.4791 0.5083 70.4934 0.1697 0.4791 0.5083 70.4934 -0.2139 0.0767 0.2272 160.271 -2.8012

295 -0.3284 -0.0173 0.3288 183.013 0.245 0.6468 0.6916 69.2549 0.245 0.6468 0.6916 69.2549 -0.2737 0.114 0.2965 157.395 -6.4386

300 -0.4022 0.0223 0.4028 176.833 0.3275 0.832 0.8941 68.5134 0.3275 0.832 0.8941 68.5134 -0.3373 0.1575 0.3722 154.963 -11.4559

305 -0.482 0.0786 0.4884 170.74 0.42 1.0409 1.1224 68.0233 0.42 1.0409 1.1224 68.0233 -0.4056 0.2094 0.4565 152.689 -18.2168

310 -0.5691 0.1577 0.5905 164.509 0.5267 1.2826 1.3866 67.6743 0.5267 1.2826 1.3866 67.6743 -0.4805 0.2727 0.5524 150.426 -27.2438

315 -0.6649 0.2683 0.7169 158.025 0.654 1.5718 1.7024 67.4094 0.654 1.5718 1.7024 67.4094 -0.5647 0.3517 0.6653 148.084 -39.3264

320 -0.7793 0.4314 0.8908 151.033 0.823 1.9499 2.1165 67.1161 0.823 1.9499 2.1165 67.1161 -0.6626 0.4617 0.8076 145.128 -56.3866

325 -0.9015 0.6561 1.115 143.951 1.0308 2.4243 2.6343 66.9648 1.0308 2.4243 2.6343 66.9648 -0.7845 0.6001 0.9877 142.588 -79.4016

330 -1.0498 1.0034 1.4522 136.293 1.3301 3.109 3.3815 66.8374 1.3301 3.109 3.3815 66.8374 -0.9484 0.8045 1.2437 139.692 -113.961

335 -1.2978 1.8488 2.2589 125.067 1.9931 4.6567 5.0653 66.8291 1.9931 4.6567 5.0653 66.8291 -1.2968 1.2729 1.8171 135.535 -193.601

340 -1.5785 3.6128 3.9426 113.601 3.1964 7.4937 8.147 66.8997 3.1964 7.4937 8.147 66.8997 -1.8258 2.1669 2.8336 130.117 -351.954

345 -1.3078 12.2608 12.33 96.0883 7.4881 18.0477 19.5395 67.4663 7.4881 18.0477 19.5395 67.4663 -3.0624 5.7307 6.4976 118.119 -1042.7

350 157.721 312.159 349.74 63.1944 0.2819 59.6333 59.634 89.7291 0.2819 59.6333 59.634 89.7291 80.3855 51.3439 95.3836 32.5672 -17175

355 4.4406 1.2802 4.6215 16.0816 -4.4001 -8.7406 9.7857 243.279 -4.4001 -8.7406 9.7857 243.279 3.6473 -2.0028 4.161 331.228 148.656

360 1.3073 -0.3779 1.3608 343.876 -1.9873 -4.1323 4.5853 244.316 -1.9873 -4.1323 4.5853 244.316 1.3118 -1.0902 1.7057 320.27 121.257

Appendix A7


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 -0.0384 3.9838 3.984 90.5525 1.532 -1.9624 2.4896 307.9785 1.1999 -1.7933 2.1577 303.7855

5 0.085 2.7432 2.7445 88.2252 0.7538 -1.1178 1.3483 303.9942 0.6864 -1.1585 1.3466 300.6482

10 0.0817 1.9938 1.9954 87.6539 0.4502 -0.7226 0.8514 301.9238 0.4398 -0.8463 0.9538 297.4613

15 0.0379 1.4808 1.4813 88.5331 0.304 -0.4865 0.5737 301.9995 0.3281 -0.6404 0.7195 297.1275

20 0.0232 1.2078 1.208 88.8999 0.2316 -0.3603 0.4284 302.7335 0.2519 -0.5431 0.5987 294.8818

25 0.0304 1.0682 1.0687 88.3675 0.194 -0.2902 0.3491 303.7679 0.2082 -0.4926 0.5348 292.9109

30 0.0627 1.025 1.0269 86.4998 0.1748 -0.2544 0.3086 304.4917 0.1844 -0.4736 0.5083 291.2716

35 0.119 1.0509 1.0576 83.5379 0.1658 -0.239 0.2909 304.7585 0.1732 -0.4763 0.5068 289.9794

40 0.2208 1.1679 1.1886 79.294 0.1639 -0.246 0.2956 303.6801 0.1446 -0.5251 0.5446 285.3927

45 0.3147 1.2715 1.3098 76.0961 0.1654 -0.2461 0.2965 303.9031 0.1461 -0.5498 0.5689 284.8783

50 0.4198 1.3926 1.4545 73.2252 0.1699 -0.2479 0.3005 304.4311 0.151 -0.5781 0.5975 284.6362

55 0.5309 1.5207 1.6107 70.7543 0.1767 -0.2493 0.3055 305.3257 0.1581 -0.6064 0.6267 284.6156

60 0.6436 1.6476 1.7688 68.6628 0.1849 -0.2492 0.3103 306.5698 0.1668 -0.6321 0.6537 284.7837

65 0.7539 1.7672 1.9213 66.8976 0.194 -0.2473 0.3143 308.1094 0.1765 -0.6534 0.6768 285.1185

70 0.8585 1.8752 2.0623 65.4015 0.2033 -0.2433 0.317 309.8807 0.1869 -0.6694 0.695 285.604

75 0.9548 1.9685 2.1878 64.1239 0.2123 -0.2372 0.3183 311.8252 0.1978 -0.6797 0.7079 286.2269

80 1.0268 1.9958 2.2445 62.7739 0.2102 -0.2003 0.2903 316.3869 0.2079 -0.6855 0.7163 286.871

85 1.1025 2.0513 2.3288 61.7431 0.2147 -0.1856 0.2838 319.157 0.2196 -0.6868 0.7211 287.7306

90 1.1668 2.0902 2.3939 60.8292 0.2173 -0.1697 0.2758 322.0145 0.2313 -0.6836 0.7216 288.6967

95 1.2191 2.1126 2.4391 60.013 0.218 -0.153 0.2663 324.9255 0.2428 -0.6759 0.7182 289.7585

100 1.2588 2.1183 2.4641 59.2795 0.2163 -0.1359 0.2554 327.8665 0.2538 -0.6643 0.7112 290.9052

105 1.2856 2.1075 2.4686 58.6166 0.2123 -0.1185 0.2431 330.8247 0.2639 -0.6491 0.7007 292.1258

110 1.2991 2.0801 2.4524 58.0145 0.2058 -0.1013 0.2293 333.7981 0.2729 -0.6304 0.687 293.4091

115 1.308 2.0383 2.4219 57.3113 0.2024 -0.0933 0.2228 335.2367 0.2709 -0.5965 0.6551 294.4277

120 1.2942 1.9764 2.3625 56.7816 0.1927 -0.0786 0.2081 337.8024 0.2741 -0.569 0.6316 295.7188

125 1.2648 1.8958 2.279 56.2897 0.1811 -0.0648 0.1923 340.3098 0.2742 -0.538 0.6039 297.0057

130 1.2178 1.7941 2.1683 55.8319 0.1679 -0.052 0.1757 342.7841 0.2705 -0.5033 0.5714 298.2536

135 1.1496 1.667 2.0249 55.4076 0.1534 -0.0403 0.1586 345.2837 0.2616 -0.4643 0.5329 299.4044

140 1.054 1.5066 1.8387 55.0234 0.1383 -0.0296 0.1414 347.9348 0.2459 -0.42 0.4867 300.3468

145 0.9186 1.2979 1.59 54.7111 0.1239 -0.0196 0.1255 350.9976 0.2202 -0.3689 0.4296 300.8276

150 0.7169 1.0096 1.2382 54.6195 0.1138 -0.0101 0.1142 354.9196 0.1786 -0.3079 0.356 300.1224

155 0.3844 0.5684 0.6862 55.9296 0.1185 -0.0003 0.1185 359.8562 0.1089 -0.2313 0.2557 295.222

160 -0.2798 -0.2389 0.3679 220.4913 0.1805 0.0107 0.1808 3.3777 -0.022 -0.1282 0.1301 260.2776

165 -2.8615 -3.0498 4.182 226.8238 0.7073 0.0346 0.7082 2.7984 -0.425 0.0344 0.4264 175.3767

170 -30.1154 -26.7817 40.3013 221.6467 10.5818 -0.3246 10.5868 358.2429 -2.816 -1.1979 3.0602 203.0448

175 -15.7959 -4.3733 16.3901 195.4755 12.6991 -1.1444 12.7506 354.8506 1.8407 -5.2622 5.5749 289.28

180 -0.1576 2.871 2.8753 93.1419 2.3227 -0.2943 2.3412 352.7793 1.0586 -1.4771 1.8173 305.6267

185 0.8236 2.7343 2.8556 73.238 1.2275 -0.1841 1.2412 351.472 0.817 -0.9312 1.2388 311.2607

190 0.9706 2.4762 2.6596 68.5966 0.8768 -0.1465 0.889 350.5122 0.6989 -0.7163 1.0008 314.2922

195 0.9539 2.2548 2.4482 67.0685 0.7169 -0.1295 0.7285 349.7586 0.626 -0.5942 0.8631 316.4899

200 0.8909 2.0698 2.2534 66.7123 0.6298 -0.1209 0.6413 349.1321 0.574 -0.5114 0.7688 318.3056

205 0.8129 1.9105 2.0763 66.9502 0.5764 -0.1163 0.588 348.5883 0.5332 -0.4488 0.6969 319.9115

210 0.7311 1.7687 1.9138 67.5407 0.5396 -0.1137 0.5514 348.0954 0.4985 -0.3981 0.6379 321.3841

215 0.6564 1.5704 1.702 67.3142 0.4597 -0.0978 0.47 347.9932 0.4369 -0.3313 0.5483 322.8268

220 0.5773 1.4505 1.5612 68.2966 0.4379 -0.0964 0.4484 347.5853 0.4079 -0.2951 0.5034 324.1092

225 0.5031 1.3369 1.4284 69.3789 0.4163 -0.095 0.427 347.1507 0.3798 -0.2627 0.4618 325.3312

230 0.4342 1.2277 1.3022 70.5215 0.3932 -0.0933 0.4041 346.6571 0.3519 -0.2329 0.4219 326.5018

235 0.371 1.1214 1.1812 71.6912 0.3675 -0.0911 0.3786 346.0718 0.3234 -0.205 0.3829 327.6306

240 0.3136 1.0168 1.0641 72.859 0.3386 -0.0885 0.35 345.3576 0.2938 -0.1784 0.3438 328.7313

245 0.2619 0.9131 0.9499 73.9985 0.3062 -0.0851 0.3178 344.4679 0.2627 -0.1527 0.3039 329.8278

250 0.2156 0.8092 0.8374 75.0847 0.2703 -0.0809 0.2821 343.3364 0.2296 -0.1274 0.2626 330.9654

255 0.1744 0.7041 0.7254 76.0913 0.2308 -0.0756 0.2429 341.8573 0.1941 -0.1022 0.2194 332.2368

260 0.1379 0.5965 0.6122 76.9863 0.188 -0.069 0.2002 339.8345 0.156 -0.0766 0.1738 333.8534

265 0.106 0.5044 0.5154 78.1265 0.1501 -0.0658 0.1639 336.3156 0.1234 -0.0551 0.1351 335.9217

270 0.0774 0.3821 0.3899 78.5508 0.0983 -0.0539 0.1121 331.264 0.0769 -0.0263 0.0813 341.1267

275 0.0453 0.2163 0.221 78.1609 0.0319 -0.0328 0.0458 314.1374 0.0461 0.0337 0.0571 36.2157

280 0.0225 0.0758 0.079 73.4971 -0.025 -0.0141 0.0287 209.4393 -0.0067 0.0662 0.0666 95.8119

285 0.0012 -0.0786 0.0786 270.8496 -0.0846 0.0094 0.0851 173.6762 -0.0628 0.1014 0.1193 121.765

290 -0.0193 -0.2513 0.2521 265.6031 -0.147 0.0391 0.1521 165.0913 -0.1224 0.1402 0.1861 131.1216

295 -0.04 -0.4485 0.4503 264.8974 -0.2127 0.0771 0.2262 160.0642 -0.1858 0.1835 0.2611 135.3537

300 -0.0624 -0.678 0.6808 264.7422 -0.2819 0.1259 0.3087 155.9346 -0.2536 0.2329 0.3443 137.4425

305 -0.0884 -0.9507 0.9548 264.6888 -0.3551 0.1888 0.4021 152.0055 -0.3268 0.2902 0.4371 138.3924

310 -0.1212 -1.2825 1.2882 264.603 -0.4325 0.2702 0.51 148.0094 -0.4068 0.3584 0.5422 138.6228

315 -0.1658 -1.6975 1.7055 264.4198 -0.5144 0.3763 0.6373 143.811 -0.4962 0.4416 0.6642 138.3348

320 -0.2345 -2.2601 2.2722 264.0753 -0.6077 0.5237 0.8022 139.2432 -0.5984 0.5544 0.8158 137.1868

325 -0.3371 -2.9907 3.0097 263.5687 -0.6953 0.7116 0.9949 134.3384 -0.7237 0.6923 1.0015 136.2699

330 -0.5134 -4.0746 4.1068 262.8182 -0.7816 0.9759 1.2503 128.6916 -0.8879 0.8884 1.256 134.9838

335 -1.0021 -6.6139 6.6893 261.3847 -0.8353 1.5134 1.7287 118.8966 -1.2251 1.3048 1.7898 133.1947

340 -2.1532 -11.6156 11.8135 259.4982 -0.6287 2.3261 2.4096 105.1238 -1.7198 1.9857 2.6269 130.8943

345 -8.39 -33.4662 34.5019 255.926 2.5423 4.2112 4.9191 58.881 -2.7817 3.7487 4.668 126.5767

350 -269.4837 -530.9699 595.4415 243.0908 302.1871 -116.0323 323.6983 338.9945 83.2552 -82.6861 117.3389 315.1965

355 -2.171 5.0572 5.5035 113.2333 6.1174 -5.5628 8.2685 317.7187 3.5076 -4.5085 5.7122 307.8828

360 -0.0384 3.9838 3.984 90.5525 1.532 -1.9624 2.4896 307.9785 1.1999 -1.7933 2.1577 303.7855

Appendix A7


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 -0.0463 -3.9876 3.9878 269.334 1.2873 -0.3612 1.3371 344.326 -1.9895 -4.1581 4.6095 244.43 1.3096 -1.1181 1.7219 319.51 121.247

5 -0.1694 -2.7543 2.7595 266.48 0.693 -0.2999 0.7551 336.602 -1.2877 -2.7275 3.0162 244.728 0.7876 -0.7583 1.0933 316.084 82.9521

10 -0.1652 -2.0122 2.019 265.308 0.4515 -0.1983 0.4931 336.285 -0.9484 -1.9967 2.2105 244.595 0.5407 -0.5563 0.7758 314.187 59.3361

15 -0.1198 -1.5065 1.5113 265.454 0.334 -0.1015 0.3491 343.1 -0.7351 -1.5505 1.7159 244.634 0.4318 -0.4044 0.5916 316.877 43.2466

20 -0.1028 -1.2405 1.2448 265.261 0.2781 -0.0498 0.2826 349.842 -0.6295 -1.3208 1.4631 244.516 0.3595 -0.3374 0.493 316.818 34.3136

25 -0.1073 -1.1078 1.113 264.47 0.2514 -0.022 0.2524 355 -0.5829 -1.2112 1.3442 244.301 0.3197 -0.3056 0.4422 316.292 29.0871

30 -0.1361 -1.0711 1.0797 262.759 0.24 -0.0107 0.2403 357.447 -0.5803 -1.1868 1.3211 243.945 0.2992 -0.2994 0.4233 314.985 26.0751

35 -0.1885 -1.1032 1.1192 260.306 0.237 -0.0093 0.2372 357.76 -0.6119 -1.2246 1.3689 243.451 0.2906 -0.3118 0.4262 312.983 24.1339

40 -0.2857 -1.2262 1.259 256.882 0.2397 -0.0239 0.2409 354.315 -0.6952 -1.3388 1.5085 242.557 0.2636 -0.3688 0.4533 305.561 22.9215

45 -0.3747 -1.3351 1.3867 254.324 0.2447 -0.0276 0.2462 353.557 -0.7731 -1.4507 1.6438 241.947 0.2659 -0.4009 0.481 303.552 20.6

50 -0.4743 -1.4613 1.5363 252.019 0.2516 -0.0307 0.2535 353.041 -0.8638 -1.5806 1.8012 241.343 0.2706 -0.4362 0.5133 301.813 17.4664

55 -0.5795 -1.5939 1.6959 250.019 0.2599 -0.0322 0.2619 352.94 -0.9615 -1.7184 1.9691 240.771 0.2768 -0.4714 0.5466 300.426 13.3191

60 -0.686 -1.7247 1.8561 248.311 0.2687 -0.0318 0.2706 353.253 -1.0609 -1.8559 2.1377 240.246 0.2839 -0.5038 0.5783 299.406 8.1171

65 -0.7897 -1.8478 2.0095 246.86 0.2776 -0.0297 0.2792 353.904 -1.1574 -1.9866 2.2991 239.774 0.2915 -0.5318 0.6064 298.734 1.9444

70 -0.8875 -1.9586 2.1503 245.624 0.286 -0.026 0.2872 354.801 -1.2473 -2.1056 2.4473 239.358 0.2994 -0.5544 0.6301 298.375 -5.0246

75 -0.9768 -2.0541 2.2745 244.568 0.2934 -0.0212 0.2941 355.865 -1.3276 -2.2094 2.5776 239 0.3074 -0.5713 0.6487 298.289 -12.5565

80 -1.0416 -2.083 2.3289 243.434 0.2909 0.011 0.2911 2.1643 -1.3727 -2.2726 2.655 238.867 0.314 -0.5836 0.6627 298.278 -20.2228

85 -1.1099 -2.1394 2.4102 242.581 0.2929 0.0221 0.2937 4.3193 -1.4265 -2.3415 2.7418 238.649 0.3224 -0.5914 0.6735 298.595 -27.9795

90 -1.1668 -2.1788 2.4715 241.829 0.2926 0.0332 0.2945 6.4744 -1.4666 -2.3919 2.8058 238.485 0.3306 -0.5944 0.6801 299.083 -35.5058

95 -1.2117 -2.2008 2.5123 241.164 0.2899 0.0438 0.2932 8.5994 -1.4925 -2.4235 2.8462 238.373 0.3384 -0.593 0.6827 299.714 -42.5594

100 -1.2441 -2.2055 2.5322 240.574 0.2847 0.0537 0.2897 10.678 -1.5036 -2.4357 2.8624 238.312 0.3456 -0.5875 0.6816 300.465 -48.9194

105 -1.2636 -2.1931 2.5311 240.05 0.277 0.0624 0.2839 12.7035 -1.4997 -2.4284 2.8541 238.301 0.3518 -0.5783 0.6769 301.313 -54.3901

110 -1.2701 -2.1635 2.5087 239.585 0.2669 0.0699 0.2759 14.6742 -1.4809 -2.4014 2.8213 238.339 0.3567 -0.5655 0.6686 302.242 -58.8024

115 -1.2722 -2.1189 2.4715 239.019 0.2604 0.0669 0.2689 14.4154 -1.4617 -2.3477 2.7655 238.093 0.3504 -0.5376 0.6417 303.095 -62.2963

120 -1.2519 -2.0536 2.4051 238.634 0.2482 0.0698 0.2579 15.709 -1.4152 -2.2779 2.6817 238.15 0.3493 -0.5156 0.6227 304.115 -64.1887

125 -1.2162 -1.969 2.3143 238.297 0.2353 0.0711 0.2458 16.8063 -1.3533 -2.1862 2.5711 238.241 0.3451 -0.4896 0.599 305.18 -64.6283

130 -1.1633 -1.8627 2.1961 238.015 0.2223 0.0709 0.2333 17.6808 -1.2753 -2.0703 2.4315 238.366 0.3373 -0.4592 0.5698 306.298 -63.4921

135 -1.0897 -1.7306 2.0451 237.803 0.2105 0.0697 0.2217 18.3165 -1.1793 -1.9266 2.2589 238.529 0.3249 -0.4235 0.5338 307.498 -60.6194

140 -0.9891 -1.5648 1.8512 237.704 0.2016 0.0684 0.2129 18.7425 -1.0614 -1.7484 2.0454 238.739 0.3067 -0.3805 0.4888 308.869 -55.7514

145 -0.8491 -1.3502 1.595 237.835 0.1989 0.0689 0.2105 19.1117 -0.9142 -1.523 1.7764 239.025 0.281 -0.327 0.4311 310.67 -48.3999

150 -0.6435 -1.0557 1.2364 238.634 0.2087 0.0753 0.2219 19.8364 -0.7217 -1.2245 1.4214 239.486 0.245 -0.2556 0.354 313.781 -37.5305

155 -0.3076 -0.608 0.6814 243.163 0.247 0.0981 0.2658 21.6633 -0.4463 -0.7938 0.9106 240.652 0.1947 -0.1492 0.2453 322.543 -20.639

160 0.3595 0.2062 0.4144 29.8369 0.3661 0.1726 0.4048 25.2436 0.0196 -0.0657 0.0685 286.587 0.1265 0.0437 0.1338 19.0645 9.7251

165 2.9434 3.0241 4.22 45.7745 0.989 0.6294 1.1723 32.4708 1.4708 2.1364 2.5937 55.4536 0.0786 0.7077 0.712 83.6622 112.16

170 30.1989 26.7632 40.352 41.5483 9.614 6.7638 11.7549 35.1277 12.1043 16.8995 20.7872 54.3877 2.8881 6.7914 7.38 66.9622 961.698

175 15.8803 4.3622 16.469 15.3597 8.1553 5.4509 9.8093 33.7584 -0.8028 -4.4531 4.5249 259.78 6.9893 2.0691 7.2891 16.4911 174.446

180 0.2424 -2.8747 2.8849 274.819 1.181 0.6452 1.3457 28.6481 -2.1227 -4.085 4.6036 242.542 1.7855 -0.4275 1.836 346.534 -87.3844

185 -0.7391 -2.7307 2.8289 254.854 0.5399 0.2032 0.5769 20.6278 -1.7364 -3.2012 3.6418 241.524 1.1192 -0.4834 1.2192 336.638 -80.7238

190 -0.8871 -2.4652 2.62 250.209 0.3574 0.0676 0.3637 10.7088 -1.4775 -2.6967 3.075 241.281 0.8662 -0.4543 0.9781 332.325 -69.0965

195 -0.872 -2.2366 2.4006 248.699 0.2845 0.0048 0.2846 0.9704 -1.2902 -2.3511 2.6818 241.244 0.7287 -0.4167 0.8395 330.235 -58.7809

200 -0.8112 -2.0445 2.1996 248.358 0.2519 -0.0308 0.2538 353.023 -1.1444 -2.088 2.3811 241.274 0.6378 -0.3813 0.7431 329.126 -49.932

205 -0.7361 -1.8784 2.0175 248.601 0.2372 -0.0533 0.2432 347.344 -1.0246 -1.8733 2.1352 241.324 0.5697 -0.3492 0.6682 328.49 -42.2534

210 -0.6577 -1.73 1.8508 249.184 0.2309 -0.068 0.2407 343.595 -0.922 -1.6891 1.9244 241.371 0.5139 -0.3201 0.6054 328.078 -35.5027

215 -0.587 -1.5255 1.6345 248.953 0.1908 -0.0859 0.2093 335.752 -0.784 -1.4378 1.6377 241.397 0.4295 -0.2828 0.5143 326.639 -27.7029

220 -0.5124 -1.3998 1.4906 249.895 0.1897 -0.0908 0.2103 334.412 -0.7047 -1.2924 1.472 241.399 0.3867 -0.2583 0.465 326.259 -22.5353

225 -0.4431 -1.2807 1.3552 250.914 0.187 -0.0931 0.2089 333.527 -0.6322 -1.1579 1.3192 241.366 0.3464 -0.2356 0.4189 325.784 -17.9561

230 -0.3797 -1.1665 1.2267 251.968 0.1815 -0.0936 0.2042 332.727 -0.5649 -1.0312 1.1758 241.289 0.3075 -0.2143 0.3748 325.136 -13.904

235 -0.3224 -1.0557 1.1038 253.016 0.1723 -0.0928 0.1957 331.691 -0.5015 -0.9103 1.0393 241.149 0.2692 -0.194 0.3319 324.22 -10.3346

240 -0.2712 -0.9472 0.9853 254.02 0.1589 -0.0914 0.1833 330.084 -0.4411 -0.7933 0.9077 240.923 0.2309 -0.1746 0.2895 322.902 -7.2164

245 -0.226 -0.8401 0.8699 254.94 0.1407 -0.0897 0.1669 327.468 -0.3828 -0.6786 0.7792 240.571 0.192 -0.1557 0.2472 320.967 -4.5297

250 -0.1866 -0.7333 0.7567 255.727 0.1176 -0.0881 0.147 323.154 -0.326 -0.565 0.6523 240.019 0.1522 -0.137 0.2048 318.022 -2.2654

255 -0.1524 -0.626 0.6443 256.315 0.0895 -0.0867 0.1245 315.907 -0.2698 -0.4512 0.5257 239.12 0.1112 -0.1181 0.1622 313.264 -0.4255

260 -0.1231 -0.5168 0.5313 256.597 0.0562 -0.0853 0.1021 303.392 -0.2138 -0.336 0.3983 237.533 0.0686 -0.0989 0.1204 304.766 0.976

265 -0.0987 -0.4237 0.435 256.892 0.0259 -0.0847 0.0886 286.988 -0.1673 -0.2386 0.2914 234.975 0.0326 -0.0822 0.0884 291.616 1.8753

270 -0.0774 -0.3011 0.3109 255.586 -0.0197 -0.0823 0.0846 256.539 -0.1069 -0.1117 0.1546 226.252 -0.0159 -0.0601 0.0622 255.146 2.355

275 -0.0527 -0.1356 0.1455 248.754 -0.0819 -0.0717 0.1089 221.191 -0.0268 0.0492 0.056 118.602 -0.0476 -0.0066 0.0481 187.951 1.95

280 -0.0372 0.0039 0.0374 173.942 -0.1366 -0.0641 0.1509 205.128 0.0363 0.1862 0.1897 78.9751 -0.1 0.0194 0.1019 169.02 1.0766

285 -0.0231 0.1567 0.1584 98.387 -0.1957 -0.0518 0.2025 194.829 0.1022 0.3308 0.3463 72.8362 -0.1546 0.0483 0.162 162.64 -0.5794

290 -0.0097 0.3272 0.3274 91.6916 -0.2595 -0.033 0.2616 187.239 0.172 0.4855 0.5151 70.4923 -0.2116 0.081 0.2265 159.059 -3.1615

295 0.0042 0.5215 0.5216 89.5358 -0.3284 -0.0049 0.3284 180.853 0.2472 0.6534 0.6986 69.2788 -0.2715 0.1185 0.2962 156.43 -6.8635

300 0.02 0.7476 0.7479 88.4668 -0.4028 0.0358 0.4044 174.922 0.3296 0.8388 0.9013 68.5459 -0.3351 0.1623 0.3723 154.163 -11.9494

305 0.0398 1.0164 1.0172 87.7593 -0.4833 0.0935 0.4923 169.05 0.4222 1.048 1.1298 68.0573 -0.4034 0.2144 0.4569 152.008 -18.7859

310 0.0667 1.3437 1.3454 87.1588 -0.5712 0.1743 0.5972 163.028 0.5289 1.2901 1.3943 67.7063 -0.4783 0.2779 0.5532 149.837 -27.8982

315 0.1059 1.7536 1.7568 86.5438 -0.668 0.287 0.727 156.75 0.6563 1.5795 1.7104 67.4372 -0.5624 0.3573 0.6663 147.572 -40.0792

320 0.1696 2.3108 2.317 85.802 -0.7836 0.4528 0.905 149.978 0.8255 1.9579 2.1249 67.1377 -0.66 0.4676 0.8089 144.683 -57.257

325 0.2677 3.0356 3.0474 84.9605 -0.9073 0.6813 1.1346 143.097 1.0337 2.4326 2.6431 66.9781 -0.7817 0.6063 0.9892 142.204 -80.4171

330 0.44 4.1133 4.1367 83.8938 -1.058 1.0344 1.4797 135.647 1.3336 3.1174 3.3907 66.8391 -0.9449 0.8108 1.2451 139.367 -115.174

335 0.9252 6.6459 6.71 82.0743 -1.3133 1.8971 2.3073 124.695 1.9985 4.6644 5.0745 66.8066 -1.2914 1.2785 1.8172 135.288 -195.272

340 2.0736 11.6409 11.824 79.9 -1.6138 3.7005 4.0371 113.563 3.2065 7.4962 8.1532 66.8411 -1.8157 2.1673 2.8273 129.955 -354.538

345 8.3081 33.4844 34.5 76.0652 -1.47 12.5766 12.6623 96.6667 7.5234 17.9972 19.5064 67.3135 -3.027 5.678 6.4345 118.063 -1049.7

350 269.4 530.981 595.41 63.0984 150.682 323.065 356.477 64.9951 1.2899 55.1435 55.1586 88.66 81.3935 46.8519 93.9149 29.9257 -17336

355 2.0866 -5.0536 5.4674 292.435 4.3434 1.4042 4.5648 17.9153 -4.3947 -8.83 9.8632 243.541 3.6527 -2.0943 4.2105 330.172 147.567

360 -0.0463 -3.9876 3.9878 269.334 1.2873 -0.3612 1.3371 344.326 -1.9895 -4.1581 4.6095 244.43 1.3096 -1.1181 1.7219 319.51 121.247

Appendix A8


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 -0.0656 3.9668 3.9674 90.9474 1.5555 -1.9752 2.5142 308.2212 1.2036 -1.7635 2.1351 304.3122

5 0.0675 2.7245 2.7253 88.5798 0.767 -1.1187 1.3564 304.4334 0.6907 -1.1389 1.332 301.2378

10 0.0675 1.9753 1.9765 88.044 0.4599 -0.7195 0.8539 302.584 0.4444 -0.831 0.9423 298.137

15 0.025 1.4626 1.4629 89.0219 0.3122 -0.4815 0.5739 302.9539 0.3329 -0.6272 0.71 297.9567

20 0.0108 1.1899 1.1899 89.4808 0.2391 -0.3545 0.4276 303.9995 0.2568 -0.5311 0.5899 295.8094

25 0.0183 1.0508 1.0509 89.0007 0.2011 -0.284 0.348 305.3006 0.2132 -0.4813 0.5264 293.8954

30 0.0509 1.0082 1.0095 87.1124 0.1815 -0.2483 0.3076 306.1742 0.1895 -0.4629 0.5002 292.2593

35 0.1075 1.035 1.0405 84.0674 0.1722 -0.2331 0.2899 306.4565 0.1782 -0.4662 0.4991 290.9222

40 0.2098 1.1531 1.172 79.6876 0.17 -0.2406 0.2946 305.2358 0.1495 -0.5156 0.5368 286.1717

45 0.3043 1.2578 1.2941 76.398 0.171 -0.2413 0.2958 305.3279 0.1508 -0.5409 0.5616 285.5807

50 0.4101 1.3802 1.4398 73.4531 0.1751 -0.2437 0.3001 305.7064 0.1555 -0.57 0.5908 285.2605

55 0.5219 1.5095 1.5972 70.9264 0.1814 -0.2456 0.3054 306.4526 0.1624 -0.599 0.6206 285.1659

60 0.6354 1.6377 1.7566 68.7941 0.1892 -0.2461 0.3104 307.5587 0.1707 -0.6253 0.6482 285.2666

65 0.7465 1.7584 1.9103 66.999 0.1979 -0.2446 0.3146 308.9739 0.18 -0.6473 0.6719 285.5413

70 0.8518 1.8675 2.0526 65.4807 0.2068 -0.241 0.3176 310.6351 0.1901 -0.664 0.6906 285.9735

75 0.9489 1.9617 2.1791 64.1862 0.2155 -0.2353 0.319 312.483 0.2005 -0.6749 0.704 286.5493

80 1.0217 1.9898 2.2368 62.8215 0.213 -0.1986 0.2912 317.0062 0.2102 -0.6812 0.7129 287.1524

85 1.098 2.0461 2.3221 61.7793 0.2171 -0.1841 0.2847 319.7013 0.2216 -0.6831 0.7181 287.9739

90 1.163 2.0857 2.388 60.8555 0.2195 -0.1685 0.2767 322.4922 0.233 -0.6803 0.719 288.9056

95 1.2159 2.1086 2.4341 60.0304 0.2198 -0.1519 0.2672 325.3442 0.2441 -0.6731 0.716 289.9362

100 1.2563 2.1148 2.4598 59.2883 0.2178 -0.1349 0.2562 328.2333 0.2548 -0.6619 0.7092 291.0542

105 1.2837 2.1044 2.465 58.6165 0.2134 -0.1176 0.2436 331.1465 0.2647 -0.647 0.699 292.2485

110 1.2979 2.0774 2.4495 58.0047 0.2065 -0.1003 0.2295 334.0823 0.2734 -0.6286 0.6855 293.5074

115 1.3075 2.036 2.4197 57.2904 0.2026 -0.0924 0.2226 335.4815 0.2712 -0.595 0.6539 294.5025

120 1.2945 1.9743 2.3608 56.7472 0.1923 -0.0776 0.2074 338.0217 0.2742 -0.5679 0.6306 295.7724

125 1.2659 1.8938 2.2779 56.2382 0.18 -0.0637 0.191 340.5134 0.2742 -0.5371 0.603 297.0402

130 1.2198 1.7921 2.1679 55.7582 0.166 -0.0508 0.1735 342.9867 0.2703 -0.5026 0.5707 298.2719

135 1.1528 1.665 2.0252 55.3041 0.1504 -0.0389 0.1554 345.5114 0.2614 -0.4637 0.5324 299.4114

140 1.0583 1.5046 1.8395 54.879 0.1342 -0.0279 0.1371 348.2387 0.2457 -0.4196 0.4863 300.3518

145 0.9238 1.2956 1.5912 54.5097 0.1187 -0.0178 0.12 351.4837 0.2201 -0.3685 0.4292 300.8516

150 0.7224 1.0067 1.2391 54.3378 0.108 -0.008 0.1083 355.7689 0.1789 -0.3072 0.3555 300.22

155 0.387 0.5644 0.6843 55.5587 0.115 0.0021 0.115 1.037 0.1099 -0.2296 0.2545 295.5748

160 -0.2929 -0.2465 0.3828 220.0819 0.1914 0.0132 0.1919 3.9318 -0.0199 -0.1231 0.1247 260.837

165 -2.9916 -3.0764 4.2912 225.8011 0.8327 0.0367 0.8335 2.5243 -0.4203 0.0589 0.4244 172.0217

170 -32.3908 -27.0914 42.2269 219.9088 12.8642 -0.3394 12.8687 358.4887 -2.8231 -0.8734 2.9551 197.191

175 -18.4681 -4.6744 19.0505 194.2036 15.4481 -1.1588 15.4915 355.7101 1.764 -4.9467 5.2518 289.6262

180 -0.6135 2.8228 2.8887 102.2613 2.8006 -0.2924 2.8158 354.0394 1.0365 -1.4308 1.7668 305.9213

185 0.6022 2.711 2.7771 77.4762 1.4632 -0.1803 1.4743 352.9742 0.8026 -0.9117 1.2146 311.3591

190 0.827 2.4606 2.5959 71.4221 1.0318 -0.1422 1.0416 352.1557 0.6874 -0.7051 0.9848 314.2705

195 0.8485 2.2429 2.398 69.2767 0.8321 -0.1249 0.8414 351.4643 0.6161 -0.587 0.8509 316.3872

200 0.8087 2.0602 2.2132 68.5681 0.7208 -0.1163 0.7301 350.8348 0.5652 -0.5064 0.7589 318.1429

205 0.7469 1.9026 2.044 68.5674 0.6504 -0.1119 0.66 350.2359 0.5251 -0.4453 0.6886 319.7014

210 0.6773 1.7623 1.8879 68.9757 0.6007 -0.1097 0.6106 349.649 0.4911 -0.3958 0.6307 321.1352

215 0.615 1.5654 1.6819 68.5527 0.5076 -0.094 0.5163 349.504 0.4305 -0.3301 0.5425 322.5153

220 0.5434 1.4468 1.5455 69.4153 0.4778 -0.0933 0.4868 348.9543 0.402 -0.2945 0.4983 323.7676

225 0.4754 1.3343 1.4165 70.3895 0.4494 -0.0925 0.4588 348.3713 0.3744 -0.2625 0.4573 324.9631

230 0.4118 1.2261 1.2934 71.4327 0.4204 -0.0914 0.4302 347.7297 0.347 -0.2331 0.418 326.1094

235 0.3531 1.1207 1.175 72.5107 0.3897 -0.09 0.3999 347.0014 0.3191 -0.2055 0.3795 327.2141

240 0.2994 1.0171 1.0602 73.5945 0.3566 -0.0879 0.3672 346.1517 0.29 -0.1792 0.3409 328.2881

245 0.2508 0.9141 0.9479 74.6588 0.3206 -0.0851 0.3317 345.135 0.2594 -0.1537 0.3015 329.3515

250 0.207 0.8108 0.8368 75.6801 0.2817 -0.0814 0.2933 343.8849 0.2267 -0.1286 0.2606 330.4429

255 0.1678 0.7063 0.7259 76.6349 0.2398 -0.0766 0.2518 342.2938 0.1917 -0.1035 0.2178 331.6431

260 0.1329 0.5992 0.6138 77.4962 0.195 -0.0704 0.2073 340.1629 0.1539 -0.078 0.1726 333.1387

265 0.1022 0.5075 0.5177 78.617 0.1557 -0.0676 0.1697 336.5486 0.1216 -0.0566 0.1341 335.0464

270 0.0744 0.3858 0.3929 79.0842 0.1028 -0.056 0.1171 331.4253 0.0754 -0.0279 0.0804 339.7198

275 0.0429 0.2205 0.2246 78.9847 0.0355 -0.0353 0.0501 315.1776 0.0448 0.032 0.0551 35.5348

280 0.0203 0.0806 0.0831 75.8353 -0.0219 -0.017 0.0277 217.9286 -0.0078 0.0644 0.0648 96.8935

285 -0.0009 -0.0731 0.0731 269.3155 -0.0817 0.0059 0.0819 175.8626 -0.0637 0.0994 0.118 122.6524

290 -0.0215 -0.245 0.2459 264.9884 -0.1441 0.035 0.1483 166.3478 -0.1231 0.1379 0.1849 131.7578

295 -0.0425 -0.441 0.4431 264.4974 -0.2095 0.0721 0.2216 161.0001 -0.1865 0.1811 0.2599 135.8471

300 -0.0653 -0.6692 0.6724 264.4302 -0.2783 0.1198 0.3031 156.7052 -0.2543 0.2302 0.343 137.8496

305 -0.0918 -0.9404 0.9449 264.4238 -0.351 0.1814 0.3951 152.6683 -0.3275 0.2873 0.4356 138.7424

310 -0.1253 -1.2703 1.2765 264.368 -0.4277 0.2612 0.5011 148.5896 -0.4076 0.3551 0.5406 138.9317

315 -0.1707 -1.6828 1.6915 264.2067 -0.5086 0.3652 0.6262 144.3198 -0.4971 0.438 0.6625 138.6119

320 -0.2404 -2.2424 2.2553 263.8812 -0.6008 0.5099 0.788 139.6776 -0.5995 0.5505 0.8139 137.4367

325 -0.3442 -2.9689 2.9888 263.3867 -0.6868 0.6939 0.9763 134.7066 -0.7251 0.6882 0.9997 136.4966

330 -0.5225 -4.0466 4.0802 262.6432 -0.7705 0.9522 1.2249 128.9807 -0.8899 0.8841 1.2544 135.1877

335 -1.0166 -6.569 6.6472 261.2032 -0.8168 1.4721 1.6835 119.0246 -1.2291 1.3013 1.79 133.3663

340 -2.183 -11.536 11.7408 259.2843 -0.5902 2.2449 2.3212 104.7293 -1.7284 1.9874 2.6339 131.0135

345 -8.5216 -33.2111 34.2869 255.6089 2.7078 3.9014 4.749 55.2371 -2.8156 3.8034 4.7321 126.5116

350 -275.5201 -524.5627 592.5178 242.2899 309.23 -126.9335 334.2684 337.6827 82.2487 -78.1922 113.4851 316.4483

355 -2.2677 5.0829 5.5658 114.0442 6.2181 -5.682 8.4232 317.5798 3.5036 -4.415 5.6363 308.4347

360 -0.0656 3.9668 3.9674 90.9474 1.5555 -1.9752 2.5142 308.2212 1.2036 -1.7635 2.1351 304.3122

Appendix A8


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 -0.0192 -3.9706 3.9706 269.724 1.3109 -0.374 1.3632 344.074 -1.9858 -4.1283 4.5811 244.311 1.3132 -1.0883 1.7056 320.351 120.73

5 -0.152 -2.7356 2.7398 266.82 0.7062 -0.3008 0.7675 336.929 -1.2834 -2.7079 2.9966 244.642 0.7918 -0.7387 1.0829 316.991 82.4308

10 -0.1509 -1.9938 1.9995 265.671 0.4611 -0.1952 0.5008 337.056 -0.9438 -1.9814 2.1947 244.531 0.5453 -0.541 0.7681 315.227 58.8592

15 -0.1068 -1.4883 1.4922 265.894 0.3422 -0.0965 0.3556 344.246 -0.7303 -1.5373 1.7019 244.588 0.4366 -0.3912 0.5862 318.14 42.8144

20 -0.0904 -1.2226 1.226 265.77 0.2856 -0.044 0.289 351.241 -0.6246 -1.3087 1.4501 244.487 0.3644 -0.3253 0.4885 318.246 33.9307

25 -0.0951 -1.0903 1.0945 265.013 0.2585 -0.0158 0.259 356.494 -0.5778 -1.1999 1.3318 244.286 0.3247 -0.2942 0.4382 317.817 28.761

30 -0.1243 -1.0543 1.0616 263.278 0.2468 -0.0046 0.2468 358.935 -0.5752 -1.1761 1.3092 243.939 0.3043 -0.2887 0.4195 316.51 25.8121

35 -0.177 -1.0873 1.1016 260.755 0.2435 -0.0035 0.2435 359.185 -0.6068 -1.2144 1.3576 243.451 0.2956 -0.3017 0.4224 314.421 23.9372

40 -0.2747 -1.2113 1.2421 257.221 0.2458 -0.0185 0.2465 355.69 -0.6903 -1.3292 1.4978 242.557 0.2686 -0.3593 0.4486 306.782 22.7904

45 -0.3643 -1.3215 1.3708 254.589 0.2503 -0.0228 0.2513 354.787 -0.7683 -1.4418 1.6337 241.948 0.2706 -0.392 0.4764 304.619 20.53

50 -0.4645 -1.4489 1.5215 252.223 0.2569 -0.0265 0.2582 354.111 -0.8593 -1.5724 1.7919 241.344 0.2751 -0.428 0.5088 302.731 17.4504

55 -0.5706 -1.5827 1.6824 250.176 0.2647 -0.0285 0.2662 353.849 -0.9573 -1.7109 1.9605 240.772 0.281 -0.4639 0.5424 301.21 13.3483

60 -0.6778 -1.7148 1.8439 248.434 0.2731 -0.0286 0.2746 354.011 -1.0571 -1.8491 2.1299 240.245 0.2878 -0.497 0.5743 300.074 8.1821

65 -0.7823 -1.839 1.9985 246.956 0.2816 -0.027 0.2828 354.529 -1.1539 -1.9805 2.2921 239.772 0.295 -0.5257 0.6028 299.303 2.0361

70 -0.8808 -1.9509 2.1405 245.701 0.2895 -0.0237 0.2905 355.312 -1.2442 -2.1001 2.441 239.356 0.3025 -0.5489 0.6268 298.861 -4.9147

75 -0.9708 -2.0473 2.2658 244.63 0.2966 -0.0193 0.2972 356.281 -1.3249 -2.2046 2.5721 238.996 0.3102 -0.5664 0.6458 298.704 -12.4361

80 -1.0364 -2.077 2.3213 243.482 0.2937 0.0127 0.294 2.47 -1.3704 -2.2683 2.6501 238.862 0.3163 -0.5793 0.6601 298.635 -20.0996

85 -1.1054 -2.1342 2.4035 242.618 0.2954 0.0236 0.2963 4.5611 -1.4245 -2.3377 2.7375 238.644 0.3244 -0.5876 0.6712 298.899 -27.858

90 -1.163 -2.1742 2.4657 241.857 0.2947 0.0345 0.2967 6.668 -1.465 -2.3886 2.8021 238.479 0.3322 -0.5911 0.678 299.34 -35.3903

95 -1.2085 -2.1968 2.5073 241.183 0.2917 0.0449 0.2951 8.7597 -1.4911 -2.4206 2.843 238.366 0.3397 -0.5901 0.6809 299.931 -42.4535

100 -1.2416 -2.202 2.5279 240.585 0.2861 0.0547 0.2913 10.8194 -1.5026 -2.4332 2.8597 238.304 0.3466 -0.585 0.68 300.645 -48.8259

105 -1.2618 -2.19 2.5275 240.052 0.2781 0.0634 0.2852 12.8406 -1.499 -2.4262 2.8519 238.291 0.3525 -0.5762 0.6755 301.461 -54.3111

110 -1.2689 -2.1608 2.5058 239.577 0.2676 0.0708 0.2769 14.8236 -1.4804 -2.3996 2.8195 238.328 0.3572 -0.5638 0.6674 302.361 -58.7397

115 -1.2717 -2.1165 2.4692 239 0.2606 0.0679 0.2693 14.6006 -1.4614 -2.3462 2.7642 238.082 0.3507 -0.5362 0.6407 303.187 -62.252

120 -1.2521 -2.0514 2.4034 238.601 0.2479 0.0708 0.2578 15.9462 -1.4151 -2.2768 2.6807 238.138 0.3494 -0.5144 0.6218 304.182 -64.1628

125 -1.2173 -1.9669 2.3132 238.247 0.2342 0.0722 0.2451 17.1238 -1.3534 -2.1852 2.5704 238.229 0.3451 -0.4887 0.5983 305.226 -64.621

130 -1.1654 -1.8608 2.1956 237.942 0.2204 0.0721 0.2319 18.1136 -1.2755 -2.0696 2.431 238.354 0.3372 -0.4586 0.5692 306.326 -63.5026

135 -1.0928 -1.7287 2.0452 237.701 0.2075 0.0711 0.2194 18.9041 -1.1795 -1.9261 2.2585 238.518 0.3247 -0.423 0.5332 307.513 -60.6456

140 -0.9933 -1.5628 1.8518 237.56 0.1975 0.07 0.2096 19.519 -1.0616 -1.748 2.0451 238.729 0.3065 -0.3802 0.4884 308.882 -55.7879

145 -0.8544 -1.348 1.5959 237.632 0.1936 0.0708 0.2062 20.0763 -0.9143 -1.5226 1.776 239.018 0.2809 -0.3266 0.4308 310.702 -48.4355

150 -0.649 -1.0529 1.2368 238.35 0.2029 0.0774 0.2172 20.8815 -0.7214 -1.2239 1.4207 239.482 0.2453 -0.2549 0.3538 313.893 -37.5398

155 -0.3102 -0.6039 0.6789 242.813 0.2435 0.1005 0.2634 22.4264 -0.4454 -0.7921 0.9087 240.65 0.1956 -0.1475 0.245 322.991 -20.5598

160 0.3725 0.2138 0.4295 29.8452 0.3771 0.1751 0.4158 24.9106 0.0217 -0.0606 0.0644 289.672 0.1286 0.0488 0.1376 20.7752 10.078

165 3.0735 3.0508 4.3305 44.7876 1.1144 0.6315 1.2809 29.5403 1.4756 2.1609 2.6166 55.6732 0.0833 0.7322 0.7369 83.5082 113.968

170 32.4743 27.0729 42.279 39.817 11.8964 6.749 13.6775 29.5668 12.0973 17.224 21.0478 54.9177 2.8811 7.116 7.6771 67.9584 983.004

175 18.5525 4.6632 19.13 14.1092 10.9042 5.4365 12.1843 26.4994 -0.8795 -4.1376 4.2301 257.999 6.9125 2.3846 7.3123 19.0329 190.66

180 0.6982 -2.8266 2.9115 283.876 1.6589 0.647 1.7806 21.3081 -2.1447 -4.0387 4.5728 242.03 1.7635 -0.3812 1.8042 347.802 -85.9182

185 -0.5178 -2.7074 2.7564 259.173 0.7756 0.207 0.8028 14.9395 -1.7508 -3.1816 3.6315 241.177 1.1048 -0.4639 1.1982 337.224 -80.6045

190 -0.7436 -2.4496 2.56 253.115 0.5124 0.072 0.5174 7.9955 -1.489 -2.6855 3.0707 240.994 0.8547 -0.4431 0.9627 332.599 -69.388

195 -0.7667 -2.2247 2.3531 250.985 0.3998 0.0095 0.3999 1.3544 -1.3 -2.3438 2.6802 240.985 0.7188 -0.4095 0.8273 330.333 -59.2611

200 -0.7291 -2.0349 2.1616 250.289 0.3429 -0.0262 0.3439 355.629 -1.1532 -2.0831 2.381 241.031 0.629 -0.3764 0.733 329.106 -50.5127

205 -0.6701 -1.8706 1.987 250.292 0.3113 -0.0489 0.3151 351.079 -1.0326 -1.8698 2.136 241.09 0.5617 -0.3458 0.6596 328.382 -42.8857

210 -0.6039 -1.7236 1.8264 250.691 0.2921 -0.064 0.299 347.648 -0.9294 -1.6867 1.9258 241.145 0.5065 -0.3178 0.5979 327.898 -36.1529

215 -0.5456 -1.5206 1.6155 250.263 0.2387 -0.0822 0.2525 340.995 -0.7905 -1.4367 1.6398 241.179 0.4231 -0.2816 0.5083 326.352 -28.3039

220 -0.4784 -1.3961 1.4758 251.083 0.2295 -0.0877 0.2457 339.09 -0.7106 -1.2918 1.4743 241.187 0.3808 -0.2577 0.4598 325.913 -23.1126

225 -0.4155 -1.2781 1.3439 251.993 0.22 -0.0906 0.2379 337.613 -0.6375 -1.1577 1.3216 241.16 0.3411 -0.2354 0.4144 325.383 -18.4953

230 -0.3574 -1.1649 1.2185 252.945 0.2087 -0.0917 0.228 336.27 -0.5697 -1.0315 1.1784 241.088 0.3027 -0.2145 0.371 324.68 -14.3947

235 -0.3045 -1.055 1.0981 253.9 0.1945 -0.0916 0.215 334.776 -0.5058 -0.9109 1.0419 240.956 0.2649 -0.1946 0.3287 323.705 -10.77

240 -0.2571 -0.9474 0.9817 254.819 0.1768 -0.0908 0.1988 332.81 -0.4449 -0.7941 0.9102 240.737 0.2271 -0.1754 0.2869 322.321 -7.5933

245 -0.215 -0.841 0.8681 255.663 0.1551 -0.0897 0.1792 329.948 -0.3862 -0.6796 0.7816 240.393 0.1887 -0.1566 0.2452 320.302 -4.8478

250 -0.178 -0.7349 0.7562 256.386 0.1291 -0.0886 0.1566 325.522 -0.3288 -0.5661 0.6547 239.849 0.1493 -0.1381 0.2034 317.245 -2.5272

255 -0.1459 -0.6282 0.6449 256.927 0.0985 -0.0876 0.1318 318.344 -0.2723 -0.4524 0.5281 238.96 0.1087 -0.1194 0.1615 312.322 -0.6354

260 -0.1182 -0.5195 0.5328 257.185 0.0633 -0.0866 0.1073 306.155 -0.2159 -0.3374 0.4006 237.386 0.0665 -0.1002 0.1203 303.576 0.8125

265 -0.0948 -0.4269 0.4373 257.479 0.0315 -0.0864 0.092 290.033 -0.169 -0.2401 0.2936 234.854 0.0308 -0.0836 0.0891 290.213 1.7498

270 -0.0744 -0.3048 0.3137 256.281 -0.0152 -0.0844 0.0858 259.769 -0.1084 -0.1133 0.1568 226.261 -0.0174 -0.0617 0.0641 254.228 2.264

275 -0.0503 -0.1398 0.1486 250.209 -0.0783 -0.0742 0.1079 223.458 -0.0281 0.0475 0.0551 120.586 -0.0488 -0.0084 0.0495 189.721 1.8876

280 -0.0351 -0.0008 0.0351 181.378 -0.1334 -0.067 0.1493 206.657 0.0352 0.1843 0.1877 79.1777 -0.1011 0.0175 0.1026 170.155 1.0385

285 -0.0211 0.1512 0.1526 97.9315 -0.1928 -0.0553 0.2006 196.001 0.1013 0.3288 0.344 72.8772 -0.1555 0.0463 0.1622 163.421 -0.596

290 -0.0075 0.3208 0.3209 91.3406 -0.2566 -0.0371 0.2593 188.229 0.1712 0.4833 0.5127 70.4909 -0.2124 0.0787 0.2265 159.657 -3.1568

295 0.0067 0.5141 0.5141 89.257 -0.3253 -0.0099 0.3254 181.74 0.2465 0.6509 0.696 69.262 -0.2722 0.116 0.2959 156.919 -6.8352

300 0.0229 0.7389 0.7392 88.2261 -0.3992 0.0297 0.4003 175.739 0.329 0.8361 0.8985 68.5234 -0.3358 0.1596 0.3718 154.581 -11.8922

305 0.0432 1.0061 1.007 87.5413 -0.4792 0.0862 0.4869 169.809 0.4215 1.045 1.1268 68.0337 -0.4041 0.2115 0.4561 152.375 -18.6914

310 0.0708 1.3315 1.3334 86.9567 -0.5664 0.1653 0.59 163.728 0.5282 1.2868 1.391 67.6841 -0.479 0.2747 0.5522 150.166 -27.7544

315 0.1108 1.739 1.7426 86.3542 -0.6622 0.2759 0.7174 157.383 0.6554 1.576 1.7068 67.4183 -0.5633 0.3538 0.6652 147.868 -39.8699

320 0.1755 2.2931 2.2998 85.6245 -0.7767 0.439 0.8921 150.525 0.8245 1.9541 2.1209 67.1238 -0.6611 0.4638 0.8076 144.95 -56.9588

325 0.2748 3.0138 3.0263 84.7904 -0.8988 0.6636 1.1172 143.56 1.0322 2.4284 2.6387 66.9714 -0.7831 0.6021 0.9878 142.443 -79.9974

330 0.4491 4.0853 4.1099 83.7271 -1.0469 1.0107 1.4552 136.01 1.3315 3.1131 3.3859 66.8427 -0.9469 0.8066 1.2439 139.577 -114.574

335 0.9397 6.601 6.6676 81.8977 -1.2948 1.8557 2.2628 124.906 1.9945 4.6608 5.0697 66.8327 -1.2954 1.2749 1.8175 135.457 -194.221

340 2.1034 11.5613 11.751 79.6888 -1.5753 3.6192 3.9472 113.522 3.1978 7.4979 8.1513 66.9018 -1.8244 2.1689 2.8342 130.068 -352.573

345 8.4398 33.2293 34.284 75.749 -1.3045 12.2668 12.336 96.0702 7.4895 18.0519 19.5438 67.467 -3.0609 5.7327 6.4987 118.1 -1043.3

350 275.437 524.574 592.49 62.2975 157.725 312.164 349.748 63.1943 0.2834 59.6374 59.6381 89.7277 80.387 51.3459 95.3859 32.5677 -17176

355 2.1833 -5.0792 5.5286 293.26 4.4441 1.285 4.6262 16.1272 -4.3986 -8.7365 9.7814 243.276 3.6488 -2.0008 4.1614 331.262 148.089

360 -0.0192 -3.9706 3.9706 269.724 1.3109 -0.374 1.3632 344.074 -1.9858 -4.1283 4.5811 244.311 1.3132 -1.0883 1.7056 320.351 120.73

Appendix A9


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 3.1683 13.5963 13.9606 76.8827 1.3904 -4.0122 4.2463 289.1127 2.0372 -2.9881 3.6165 304.2845

5 2.2494 8.5507 8.8416 75.261 0.695 -2.3931 2.492 286.1935 1.2367 -1.9763 2.3314 302.0365

10 1.7997 6.0924 6.3527 73.5426 0.3914 -1.6138 1.6606 283.6336 0.8329 -1.4545 1.676 299.7961

15 1.5231 4.6682 4.9104 71.9298 0.2341 -1.1491 1.1727 281.5143 0.6331 -1.1288 1.2942 299.2857

20 1.3848 3.8843 4.1238 70.3783 0.1516 -0.8763 0.8893 279.8181 0.5066 -0.9649 1.0898 297.7004

25 1.3363 3.4678 3.7164 68.9261 0.1062 -0.7069 0.7148 278.5444 0.4351 -0.8833 0.9846 296.2268

30 1.3599 3.2964 3.5659 67.5816 0.0808 -0.5999 0.6053 277.6664 0.3976 -0.8581 0.9458 294.8606

35 1.442 3.2926 3.5945 66.3494 0.0667 -0.53 0.5342 277.1679 0.3816 -0.8722 0.9521 293.6307

40 1.5944 3.4453 3.7963 65.1664 0.0603 -0.4924 0.4961 276.9776 0.354 -0.9441 1.0083 290.5526

45 1.7562 3.6263 4.0292 64.1597 0.0576 -0.4538 0.4574 277.2314 0.3601 -0.9986 1.0616 289.8303

50 1.9395 3.8493 4.3103 63.2589 0.058 -0.4205 0.4245 277.8513 0.372 -1.0592 1.1227 289.3528

55 2.1334 4.0905 4.6134 62.4562 0.0604 -0.3897 0.3943 278.8111 0.3878 -1.1192 1.1845 289.1118

60 2.3281 4.3317 4.9177 61.7438 0.0639 -0.3598 0.3654 280.0748 0.4063 -1.1736 1.2419 289.0952

65 2.5153 4.5592 5.207 61.1142 0.0678 -0.3303 0.3371 281.6019 0.4266 -1.2191 1.2916 289.2882

70 2.6882 4.7631 5.4693 60.5605 0.0714 -0.301 0.3094 283.3519 0.4484 -1.254 1.3318 289.6745

75 2.8412 4.9363 5.6956 60.0764 0.0743 -0.272 0.282 285.2873 0.471 -1.2777 1.3617 290.2372

80 2.9419 4.961 5.7677 59.3313 0.0571 -0.176 0.1851 287.9768 0.4921 -1.2937 1.3842 290.8264

85 3.0478 5.053 5.901 58.903 0.0517 -0.137 0.1464 290.6858 0.5166 -1.2999 1.3988 291.674

90 3.1275 5.1093 5.9905 58.5284 0.044 -0.0998 0.1091 293.8203 0.5411 -1.2968 1.4052 292.6505

95 3.1797 5.1293 6.0349 58.205 0.0342 -0.065 0.0735 297.7245 0.5652 -1.2852 1.404 293.7406

100 3.2033 5.1127 6.0333 57.931 0.0223 -0.0332 0.04 303.8692 0.5883 -1.2656 1.3957 294.9293

105 3.1978 5.0595 5.9853 57.7052 0.0086 -0.0046 0.0097 331.9186 0.6096 -1.2388 1.3807 296.2025

110 3.1627 4.9696 5.8906 57.5264 -0.0065 0.0205 0.0215 107.6959 0.6286 -1.2052 1.3593 297.5464

115 3.1164 4.8469 5.7623 57.2602 -0.0111 0.0231 0.0256 115.683 0.6244 -1.1402 1.3 298.7066

120 3.0227 4.6811 5.5722 57.1484 -0.0241 0.037 0.0442 123.1088 0.631 -1.0885 1.2582 300.0992

125 2.8974 4.475 5.3311 57.0786 -0.0364 0.0467 0.0592 127.9343 0.6312 -1.0295 1.2076 301.5116

130 2.7384 4.2249 5.0348 57.0504 -0.0471 0.052 0.0702 132.1564 0.6233 -0.9624 1.1466 302.928

135 2.5421 3.9239 4.6754 57.0628 -0.0556 0.0532 0.077 136.2363 0.6049 -0.8857 1.0726 304.3305

140 2.3015 3.5596 4.2388 57.1143 -0.061 0.0506 0.0792 140.3242 0.5726 -0.797 0.9814 305.6964

145 2.0032 3.1087 3.6982 57.2037 -0.0619 0.0444 0.0762 144.356 0.5207 -0.6912 0.8654 306.9921

150 1.6189 2.5256 2.9999 57.3399 -0.0555 0.0352 0.0657 147.618 0.4388 -0.5585 0.7103 308.1514

155 1.0833 1.7094 2.0238 57.6357 -0.0325 0.0234 0.04 144.205 0.3049 -0.377 0.4849 308.9608

160 0.2096 0.3949 0.4471 62.038 0.0445 0.0097 0.0455 12.2817 0.0629 -0.0875 0.1078 305.6958

165 -2.3303 -3.209 3.9659 234.0131 0.4895 0.0162 0.4898 1.8923 -0.6443 0.7083 0.9575 132.2908

170 -19.9627 -20.2308 28.4218 225.3822 8.9342 0.0579 8.9344 0.3716 -4.042 5.1125 6.5173 128.3304

175 2.5074 22.5138 22.653 83.645 11.35 -0.2543 11.3529 358.7167 4.8826 -3.5081 6.0122 324.3028

180 3.8477 10.3192 11.0132 69.5511 2.1611 -0.1215 2.1645 356.7809 2.2676 -1.9193 2.9708 319.7546

185 3.0179 7.4118 8.0026 67.845 1.1963 -0.1078 1.2011 354.8524 1.6872 -1.4017 2.1935 320.281

190 2.4742 6.0495 6.5359 67.7561 0.9005 -0.1107 0.9073 352.9939 1.4129 -1.1507 1.8222 320.8405

195 2.0737 5.1977 5.5961 68.2496 0.7744 -0.1177 0.7833 351.3612 1.2435 -0.988 1.5882 321.5296

200 1.7567 4.5827 4.9078 69.0265 0.7107 -0.1259 0.7218 349.9554 1.1207 -0.8683 1.4177 322.2331

205 1.4942 4.0969 4.3609 69.9631 0.6734 -0.1342 0.6866 348.7312 1.022 -0.7729 1.2814 322.9037

210 1.2707 3.6891 3.9018 70.9935 0.6469 -0.1418 0.6623 347.6334 0.9367 -0.6927 1.165 323.5158

215 1.0094 3.1033 3.2634 71.9815 0.5783 -0.1254 0.5917 347.7675 0.8026 -0.5875 0.9947 323.798

220 0.8459 2.7888 2.9143 73.1259 0.556 -0.1295 0.5708 346.8897 0.7306 -0.5267 0.9007 324.2098

225 0.7035 2.4983 2.5955 74.2739 0.53 -0.132 0.5462 346.0124 0.6612 -0.4715 0.8121 324.5096

230 0.5789 2.2244 2.2985 75.4127 0.4994 -0.1328 0.5168 345.1087 0.593 -0.4202 0.7268 324.6757

235 0.4697 1.9615 2.0169 76.5342 0.4635 -0.1315 0.4818 344.1612 0.5248 -0.3719 0.6432 324.6776

240 0.3738 1.7048 1.7453 77.6345 0.422 -0.1278 0.4409 343.1583 0.4557 -0.3255 0.56 324.467

245 0.2895 1.4506 1.4792 78.7142 0.3747 -0.1211 0.3938 342.0915 0.3851 -0.2802 0.4762 323.962

250 0.2155 1.1953 1.2146 79.7805 0.3213 -0.1109 0.3399 340.9526 0.3123 -0.2353 0.391 323.0055

255 0.1506 0.9358 0.9478 80.8551 0.2617 -0.0967 0.279 339.7304 0.2367 -0.19 0.3035 321.2504

260 0.0939 0.6687 0.6753 82.0031 0.1957 -0.0775 0.2104 338.4031 0.158 -0.1436 0.2135 317.7322

265 0.0526 0.4434 0.4465 83.2322 0.1357 -0.0604 0.1486 335.9963 0.0907 -0.104 0.138 311.086

270 0.0067 0.1361 0.1362 87.1795 0.0525 -0.0255 0.0584 334.1053 0.0004 -0.0509 0.0509 270.4919

275 -0.0392 -0.2232 0.2266 260.0311 -0.0499 0.0239 0.0554 154.4208 -0.0749 0.0353 0.0827 154.7646

280 -0.0731 -0.5674 0.5721 262.6625 -0.1479 0.0771 0.1668 152.4578 -0.173 0.0963 0.198 150.9039

285 -0.1029 -0.9378 0.9434 263.7396 -0.254 0.1423 0.2912 150.7388 -0.2756 0.163 0.3201 149.403

290 -0.1302 -1.3417 1.348 264.4555 -0.3689 0.2222 0.4307 148.9388 -0.3833 0.237 0.4506 148.2737

295 -0.1572 -1.7888 1.7957 264.9763 -0.4935 0.3204 0.5884 147.0074 -0.4972 0.3204 0.5915 147.1978

300 -0.1868 -2.2923 2.2999 265.3414 -0.6289 0.4416 0.7684 144.9217 -0.6188 0.4162 0.7457 146.0745

305 -0.223 -2.8702 2.8789 265.5575 -0.7765 0.5922 0.9765 142.6672 -0.7504 0.5282 0.9176 144.8599

310 -0.2719 -3.5492 3.5596 265.6185 -0.9385 0.781 1.221 140.2337 -0.8957 0.662 1.1138 143.5307

315 -0.3429 -4.3699 4.3834 265.5131 -1.1187 1.0209 1.5145 137.6156 -1.0608 0.8266 1.3448 142.073

320 -0.4577 -5.4496 5.4688 265.1993 -1.3385 1.3476 1.8993 134.8058 -1.2538 1.0521 1.6367 139.9989

325 -0.6273 -6.7983 6.8272 264.7281 -1.5779 1.7633 2.3662 131.8251 -1.4996 1.3302 2.0045 138.4251

330 -0.909 -8.7176 8.7648 264.047 -1.8844 2.3542 3.0155 128.6754 -1.837 1.7329 2.5253 136.6695

335 -1.6199 -12.9211 13.0223 262.854 -2.4649 3.629 4.3869 124.1851 -2.586 2.6212 3.6822 134.6124

340 -2.9375 -20.0894 20.303 261.6811 -3.4182 5.6976 6.6443 120.9611 -3.841 4.1951 5.6879 132.4764

345 -7.5229 -43.0244 43.6772 260.082 -6.2209 11.922 13.4474 117.5556 -7.9222 9.4365 12.3211 130.0142

350 27.8087 312.3277 313.5632 84.912 67.639 -129.7592 146.33 297.5315 43.8886 -43.2155 61.5938 315.4427

355 6.378 33.0504 33.6601 79.0774 4.3435 -10.3738 11.2464 292.7189 5.1522 -6.8024 8.5334 307.1407

360 3.1683 13.5963 13.9606 76.8827 1.3904 -4.0122 4.2463 289.1127 2.0372 -2.9881 3.6165 304.2845

Appendix A9


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 -3.1683 -13.596 13.961 256.883 1.3904 -4.0122 4.2463 289.113 -4.5595 -9.5848 10.614 244.56 2.0372 -2.9881 3.6165 304.285 413.736

5 -2.2494 -8.5507 8.8416 255.261 0.695 -2.3931 2.492 286.194 -2.945 -6.158 6.826 244.441 1.2367 -1.9763 2.3314 302.037 253.241

10 -1.7997 -6.0924 6.3527 253.543 0.3914 -1.6138 1.6606 283.634 -2.1916 -4.4789 4.9864 243.927 0.8329 -1.4545 1.676 299.796 173.065

15 -1.5231 -4.6682 4.9104 251.93 0.2341 -1.1491 1.1727 281.514 -1.7576 -3.5194 3.9339 243.463 0.6331 -1.1288 1.2942 299.286 125.216

20 -1.3848 -3.8843 4.1238 250.378 0.1516 -0.8763 0.8893 279.818 -1.5368 -3.0083 3.3782 242.94 0.5066 -0.9649 1.0898 297.7 96.6593

25 -1.3363 -3.4678 3.7164 248.926 0.1062 -0.7069 0.7148 278.544 -1.4429 -2.7613 3.1155 242.411 0.4351 -0.8833 0.9846 296.227 78.4537

30 -1.3599 -3.2964 3.5659 247.582 0.0808 -0.5999 0.6053 277.666 -1.441 -2.6968 3.0576 241.882 0.3976 -0.8581 0.9458 294.861 66.1793

35 -1.442 -3.2926 3.5945 246.349 0.0667 -0.53 0.5342 277.168 -1.5089 -2.7628 3.148 241.359 0.3816 -0.8722 0.9521 293.631 56.9054

40 -1.5944 -3.4453 3.7963 245.166 0.0603 -0.4924 0.4961 276.978 -1.6549 -2.9531 3.3852 240.733 0.354 -0.9441 1.0083 290.553 49.1253

45 -1.7562 -3.6263 4.0292 244.16 0.0576 -0.4538 0.4574 277.231 -1.814 -3.1727 3.6547 240.241 0.3601 -0.9986 1.0616 289.83 40.24

50 -1.9395 -3.8493 4.3103 243.259 0.058 -0.4205 0.4245 277.851 -1.9977 -3.429 3.9685 239.775 0.372 -1.0592 1.1227 289.353 30.0824

55 -2.1334 -4.0905 4.6134 242.456 0.0604 -0.3897 0.3943 278.811 -2.194 -3.701 4.3025 239.34 0.3878 -1.1192 1.1845 289.112 18.2178

60 -2.3281 -4.3317 4.9177 241.744 0.0639 -0.3598 0.3654 280.075 -2.3922 -3.9721 4.6369 238.941 0.4063 -1.1736 1.2419 289.095 4.5538

65 -2.5153 -4.5592 5.207 241.114 0.0678 -0.3303 0.3371 281.602 -2.5833 -4.2291 4.9557 238.581 0.4266 -1.2191 1.2916 289.288 -10.7379

70 -2.6882 -4.7631 5.4693 240.561 0.0714 -0.301 0.3094 283.352 -2.7598 -4.4622 5.2467 238.264 0.4484 -1.254 1.3318 289.675 -27.2957

75 -2.8412 -4.9363 5.6956 240.076 0.0743 -0.272 0.282 285.287 -2.9157 -4.6645 5.5008 237.991 0.471 -1.2777 1.3617 290.237 -44.6344

80 -2.9419 -4.961 5.7677 239.331 0.0571 -0.176 0.1851 287.977 -2.9992 -4.7851 5.6473 237.921 0.4921 -1.2937 1.3842 290.826 -61.9491

85 -3.0478 -5.053 5.901 238.903 0.0517 -0.137 0.1464 290.686 -3.0996 -4.9161 5.8117 237.769 0.5166 -1.2999 1.3988 291.674 -78.9899

90 -3.1275 -5.1093 5.9905 238.528 0.044 -0.0998 0.1091 293.82 -3.1717 -5.0096 5.9292 237.662 0.5411 -1.2968 1.4052 292.651 -95.1698

95 -3.1797 -5.1293 6.0349 238.205 0.0342 -0.065 0.0735 297.725 -3.2139 -5.0643 5.9981 237.6 0.5652 -1.2852 1.404 293.741 -109.993

100 -3.2033 -5.1127 6.0333 237.931 0.0223 -0.0332 0.04 303.869 -3.2257 -5.0796 6.0172 237.583 0.5883 -1.2656 1.3957 294.929 -123.012

105 -3.1978 -5.0595 5.9853 237.705 0.0086 -0.0046 0.0097 331.919 -3.2065 -5.0549 5.9861 237.612 0.6096 -1.2388 1.3807 296.203 -133.841

110 -3.1627 -4.9696 5.8906 237.526 -0.0065 0.0205 0.0215 107.696 -3.1563 -4.99 5.9045 237.686 0.6286 -1.2052 1.3593 297.546 -142.16

115 -3.1164 -4.8469 5.7623 237.26 -0.0111 0.0231 0.0256 115.683 -3.1053 -4.87 5.7758 237.476 0.6244 -1.1402 1.3 298.707 -148.279

120 -3.0227 -4.6811 5.5722 237.148 -0.0241 0.037 0.0442 123.109 -2.9986 -4.7181 5.5903 237.562 0.631 -1.0885 1.2582 300.099 -150.88

125 -2.8974 -4.475 5.3311 237.079 -0.0364 0.0467 0.0592 127.934 -2.861 -4.5217 5.3508 237.677 0.6312 -1.0295 1.2076 301.512 -150.329

130 -2.7384 -4.2249 5.0348 237.05 -0.0471 0.052 0.0702 132.156 -2.6913 -4.2769 5.0532 237.82 0.6233 -0.9624 1.1466 302.928 -146.474

135 -2.5421 -3.9239 4.6754 237.063 -0.0556 0.0532 0.077 136.236 -2.4865 -3.9771 4.6904 237.987 0.6049 -0.8857 1.0726 304.331 -139.131

140 -2.3015 -3.5596 4.2388 237.114 -0.061 0.0506 0.0792 140.324 -2.2405 -3.6101 4.2488 238.176 0.5726 -0.797 0.9814 305.696 -127.994

145 -2.0032 -3.1087 3.6982 237.204 -0.0619 0.0444 0.0762 144.356 -1.9411 -3.1531 3.7027 238.382 0.5207 -0.6912 0.8654 306.992 -112.454

150 -1.6189 -2.5256 2.9999 237.34 -0.0555 0.0352 0.0657 147.618 -1.5634 -2.5607 3.0002 238.595 0.4388 -0.5585 0.7103 308.151 -91.1896

155 -1.0833 -1.7094 2.0238 237.636 -0.0325 0.0234 0.04 144.205 -1.0508 -1.7328 2.0265 238.766 0.3049 -0.377 0.4849 308.961 -61.0748

160 -0.2096 -0.3949 0.4471 242.038 0.0445 0.0097 0.0455 12.2817 -0.2545 -0.4049 0.4782 237.851 0.0629 -0.0875 0.1078 305.696 -13.4744

165 2.3303 3.209 3.9659 54.0131 0.4895 0.0162 0.4898 1.8923 1.8376 3.1902 3.6816 60.0574 -0.6443 0.7083 0.9575 132.291 112.676

170 19.9627 20.2308 28.422 45.3822 8.9342 0.0579 8.9344 0.3716 10.9755 20.13 22.9276 61.3993 -4.042 5.1125 6.5173 128.33 711.757

175 -2.5074 -22.514 22.653 263.645 11.35 -0.2543 11.3529 358.717 -13.9178 -22.3085 26.294 238.041 4.8826 -3.5081 6.0122 324.303 -689.139

180 -3.8477 -10.319 11.013 249.551 2.1611 -0.1215 2.1645 356.781 -6.0189 -10.2058 11.8485 239.47 2.2676 -1.9193 2.9708 319.755 -314.013

185 -3.0179 -7.4118 8.0026 247.845 1.1963 -0.1078 1.2011 354.852 -4.219 -7.3079 8.4384 240.001 1.6872 -1.4017 2.1935 320.281 -216.679

190 -2.4742 -6.0495 6.5359 247.756 0.9005 -0.1107 0.9073 352.994 -3.3778 -5.9414 6.8345 240.381 1.4129 -1.1507 1.8222 320.841 -168.217

195 -2.0737 -5.1977 5.5961 248.25 0.7744 -0.1177 0.7833 351.361 -2.8504 -5.0819 5.8267 240.712 1.2435 -0.988 1.5882 321.53 -136.445

200 -1.7567 -4.5827 4.9078 249.027 0.7107 -0.1259 0.7218 349.955 -2.4692 -4.4582 5.0964 241.02 1.1207 -0.8683 1.4177 322.233 -112.758

205 -1.4942 -4.0969 4.3609 249.963 0.6734 -0.1342 0.6866 348.731 -2.169 -3.9639 4.5185 241.313 1.022 -0.7729 1.2814 322.904 -93.7737

210 -1.2707 -3.6891 3.9018 250.994 0.6469 -0.1418 0.6623 347.633 -1.9188 -3.5482 4.0338 241.596 0.9367 -0.6927 1.165 323.516 -77.8845

215 -1.0094 -3.1033 3.2634 251.982 0.5783 -0.1254 0.5917 347.768 -1.5886 -2.9787 3.3759 241.928 0.8026 -0.5875 0.9947 323.798 -59.7377

220 -0.8459 -2.7888 2.9143 253.126 0.556 -0.1295 0.5708 346.89 -1.4026 -2.6599 3.0071 242.197 0.7306 -0.5267 0.9007 324.21 -48.4627

225 -0.7035 -2.4983 2.5955 254.274 0.53 -0.132 0.5462 346.012 -1.2341 -2.3668 2.6692 242.461 0.6612 -0.4715 0.8121 324.51 -38.6202

230 -0.5789 -2.2244 2.2985 255.413 0.4994 -0.1328 0.5168 345.109 -1.0788 -2.092 2.3538 242.721 0.593 -0.4202 0.7268 324.676 -30.0155

235 -0.4697 -1.9615 2.0169 256.534 0.4635 -0.1315 0.4818 344.161 -0.9336 -1.8303 2.0546 242.974 0.5248 -0.3719 0.6432 324.678 -22.5278

240 -0.3738 -1.7048 1.7453 257.635 0.422 -0.1278 0.4409 343.158 -0.7961 -1.5773 1.7668 243.219 0.4557 -0.3255 0.56 324.467 -16.0891

245 -0.2895 -1.4506 1.4792 258.714 0.3747 -0.1211 0.3938 342.092 -0.6644 -1.3297 1.4865 243.45 0.3851 -0.2802 0.4762 323.962 -10.6713

250 -0.2155 -1.1953 1.2146 259.781 0.3213 -0.1109 0.3399 340.953 -0.537 -1.0845 1.2102 243.658 0.3123 -0.2353 0.391 323.006 -6.2786

255 -0.1506 -0.9358 0.9478 260.855 0.2617 -0.0967 0.279 339.73 -0.4125 -0.8392 0.9351 243.824 0.2367 -0.19 0.3035 321.25 -2.9422

260 -0.0939 -0.6687 0.6753 262.003 0.1957 -0.0775 0.2104 338.403 -0.2897 -0.5913 0.6585 243.9 0.158 -0.1436 0.2135 317.732 -0.7182

265 -0.0526 -0.4434 0.4465 263.232 0.1357 -0.0604 0.1486 335.996 -0.1884 -0.383 0.4268 243.812 0.0907 -0.104 0.138 311.086 0.4192

270 -0.0067 -0.1361 0.1362 267.18 0.0525 -0.0255 0.0584 334.105 -0.0593 -0.1106 0.1254 241.813 0.0004 -0.0509 0.0509 270.492 0.204

275 0.0392 0.2232 0.2266 80.0311 -0.0499 0.0239 0.0554 154.421 0.0892 0.1993 0.2184 65.892 -0.0749 0.0353 0.0827 154.765 -1.7814

280 0.0731 0.5674 0.5721 82.6625 -0.1479 0.0771 0.1668 152.458 0.221 0.4903 0.5378 65.7329 -0.173 0.0963 0.198 150.904 -5.1877

285 0.1029 0.9378 0.9434 83.7396 -0.254 0.1423 0.2912 150.739 0.357 0.7955 0.8719 65.8323 -0.2756 0.163 0.3201 149.403 -10.4094

290 0.1302 1.3417 1.348 84.4555 -0.3689 0.2222 0.4307 148.939 0.4993 1.1195 1.2258 65.9653 -0.3833 0.237 0.4506 148.274 -17.6879

295 0.1572 1.7888 1.7957 84.9763 -0.4935 0.3204 0.5884 147.007 0.6509 1.4685 1.6063 66.0963 -0.4972 0.3204 0.5915 147.198 -27.3416

300 0.1868 2.2923 2.2999 85.3414 -0.6289 0.4416 0.7684 144.922 0.8158 1.8508 2.0226 66.2131 -0.6188 0.4162 0.7457 146.075 -39.7994

305 0.223 2.8702 2.8789 85.5575 -0.7765 0.5922 0.9765 142.667 0.9996 2.2781 2.4878 66.3091 -0.7504 0.5282 0.9176 144.86 -55.6551

310 0.2719 3.5492 3.5596 85.6185 -0.9385 0.781 1.221 140.234 1.2106 2.7683 3.0215 66.3795 -0.8957 0.662 1.1138 143.531 -75.7615

315 0.3429 4.3699 4.3834 85.5131 -1.1187 1.0209 1.5145 137.616 1.4618 3.3491 3.6542 66.4202 -1.0608 0.8266 1.3448 142.073 -101.407

320 0.4577 5.4496 5.4688 85.1993 -1.3385 1.3476 1.8993 134.806 1.7963 4.1022 4.4783 66.3514 -1.2538 1.0521 1.6367 139.999 -135.986

325 0.6273 6.7983 6.8272 84.7281 -1.5779 1.7633 2.3662 131.825 2.2055 5.0352 5.497 66.3461 -1.4996 1.3302 2.0045 138.425 -180.408

330 0.909 8.7176 8.7648 84.047 -1.8844 2.3542 3.0155 128.675 2.7937 6.3636 6.9498 66.2977 -1.837 1.7329 2.5253 136.67 -243.566

335 1.6199 12.9211 13.022 82.854 -2.4649 3.629 4.3869 124.185 4.0852 9.2924 10.1507 66.2686 -2.586 2.6212 3.6822 134.612 -377.184

340 2.9375 20.0894 20.303 81.6811 -3.4182 5.6976 6.6443 120.961 6.356 14.3921 15.7332 66.1721 -3.841 4.1951 5.6879 132.476 -605.026

345 7.5229 43.0244 43.677 80.082 -6.2209 11.922 13.4474 117.556 13.7436 31.1023 34.0036 66.1601 -7.9222 9.4365 12.3211 130.014 -1323.9

350 -27.809 -312.33 313.56 264.912 67.639 -129.76 146.33 297.532 -95.5333 -182.637 206.114 242.387 43.8886 -43.216 61.5938 315.443 9506.7

355 -6.378 -33.05 33.66 259.077 4.3435 -10.374 11.2464 292.719 -10.7238 -22.6784 25.086 244.692 5.1522 -6.8024 8.5334 307.141 1018.8

360 -3.1683 -13.596 13.961 256.883 1.3904 -4.0122 4.2463 289.113 -4.5595 -9.5848 10.614 244.56 2.0372 -2.9881 3.6165 304.285 413.736

Appendix A10


theta2

degree

F12x

/10.^6

N

F12y

/10.^6

N

F12

/10.^6

N

theta12

degree

F14x

/10.^6

N

F14y

/10.^6

N

F14

/10.^6

N

theta14

degree

F16x

/10.^6

N

F16y

/10.^6

N

F16

/10.^6

N

theta16

degree

0 -0.3603 0.2109 0.4175 149.6614 0.4863 -0.3796 0.6169 322.0247 0.2828 -0.3877 0.4798 306.1117

5 -0.2084 0.2217 0.3043 133.222 0.2386 -0.1997 0.3111 320.0599 0.1577 -0.2427 0.2894 303.0154

10 -0.1613 0.1693 0.2338 133.6088 0.1456 -0.1183 0.1876 320.9001 0.0997 -0.1733 0.2 299.8983

15 -0.1459 0.1172 0.1872 141.2384 0.1027 -0.0729 0.1259 324.6316 0.0708 -0.1319 0.1497 298.2327

20 -0.1372 0.0867 0.1623 147.7167 0.0816 -0.0493 0.0953 328.8434 0.0531 -0.1103 0.1224 295.7174

25 -0.129 0.0728 0.1481 150.5512 0.0709 -0.0381 0.0805 331.748 0.0429 -0.0988 0.1077 293.4565

30 -0.118 0.0731 0.1388 148.2408 0.0655 -0.0345 0.0741 332.2163 0.0372 -0.0942 0.1013 291.5293

35 -0.1033 0.0844 0.1334 140.7669 0.0631 -0.0356 0.0725 330.6099 0.0343 -0.0943 0.1004 289.9726

40 -0.0824 0.108 0.1358 127.33 0.0626 -0.0402 0.0744 327.2926 0.0306 -0.1008 0.1054 286.9098

45 -0.0606 0.1324 0.1456 114.5796 0.0631 -0.0446 0.0773 324.7318 0.0306 -0.1059 0.1102 286.1255

50 -0.0364 0.1597 0.1638 102.8325 0.0645 -0.0492 0.0812 322.6631 0.0313 -0.1119 0.1161 285.6321

55 -0.0107 0.188 0.1883 93.2671 0.0666 -0.0534 0.0853 321.2722 0.0324 -0.1179 0.1223 285.3803

60 0.0155 0.2157 0.2163 85.8898 0.0691 -0.0568 0.0895 320.5488 0.0339 -0.1235 0.128 285.3354

65 0.0416 0.2419 0.2455 80.2534 0.0719 -0.0595 0.0933 320.4005 0.0355 -0.1281 0.133 285.4725

70 0.0668 0.2657 0.274 75.8904 0.0748 -0.0612 0.0966 320.7161 0.0372 -0.1317 0.1369 285.7725

75 0.0907 0.2867 0.3007 72.4376 0.0777 -0.062 0.0994 321.3937 0.039 -0.1341 0.1397 286.22

80 0.1102 0.2959 0.3158 69.5789 0.0782 -0.0572 0.0969 323.8001 0.0407 -0.1354 0.1413 286.7219

85 0.1306 0.3097 0.3361 67.1408 0.0801 -0.0556 0.0975 325.2531 0.0426 -0.1358 0.1424 287.4258

90 0.149 0.3203 0.3533 65.055 0.0815 -0.0532 0.0973 326.8693 0.0446 -0.1353 0.1425 288.2439

95 0.1654 0.3279 0.3672 63.2342 0.0823 -0.0502 0.0964 328.6041 0.0465 -0.1339 0.1417 289.166

100 0.1796 0.3323 0.3777 61.615 0.0824 -0.0468 0.0948 330.4257 0.0484 -0.1316 0.1402 290.1827

105 0.1915 0.3338 0.3848 60.1503 0.0817 -0.0429 0.0923 332.3131 0.0501 -0.1285 0.1379 291.2847

110 0.2012 0.3322 0.3884 58.8042 0.0802 -0.0387 0.089 334.2557 0.0516 -0.1248 0.135 292.4625

115 0.2101 0.3282 0.3897 57.3687 0.0787 -0.0359 0.0865 335.5117 0.0511 -0.1181 0.1286 293.3852

120 0.2148 0.3202 0.3856 56.1537 0.0756 -0.0315 0.0819 337.3826 0.0515 -0.1125 0.1237 294.5982

125 0.2164 0.3088 0.377 54.9818 0.0715 -0.027 0.0765 339.2968 0.0514 -0.1062 0.118 295.822

130 0.2143 0.2932 0.3632 53.8338 0.0666 -0.0225 0.0703 341.2979 0.0506 -0.0992 0.1114 297.0181

135 0.2077 0.2725 0.3426 52.6897 0.0608 -0.018 0.0635 343.4796 0.0489 -0.0914 0.1037 298.1164

140 0.1945 0.2447 0.3126 51.526 0.0544 -0.0135 0.0561 346.0422 0.0458 -0.0827 0.0945 298.9741

145 0.171 0.2061 0.2678 50.3134 0.0479 -0.009 0.0488 349.4181 0.0408 -0.0728 0.0834 299.2497

150 0.1292 0.1487 0.197 49.0251 0.0428 -0.0042 0.043 354.435 0.0326 -0.0614 0.0695 297.9445

155 0.0479 0.0532 0.0716 47.9644 0.0435 0.0012 0.0435 1.5493 0.0185 -0.0481 0.0515 291.0389

160 -0.1408 -0.1397 0.1984 224.7616 0.0689 0.0078 0.0694 6.44 -0.0089 -0.0331 0.0343 254.8728

165 -0.9987 -0.9077 1.3495 222.2675 0.3013 0.0226 0.3021 4.2846 -0.0982 -0.0326 0.1035 198.334

170 -11.5803 -8.7052 14.4873 216.9332 4.6514 -0.0325 4.6515 359.5993 -0.7419 -0.7398 1.0477 224.9208

175 -8.3643 -3.9618 9.2551 205.3452 5.5168 -0.3199 5.526 356.6817 0.1798 -1.508 1.5187 276.798

180 -0.7521 0.1286 0.763 170.2991 0.9803 -0.0839 0.9839 355.1062 0.1822 -0.3584 0.4021 296.9505

185 -0.1191 0.3601 0.3793 108.3005 0.4998 -0.0506 0.5023 354.2236 0.1506 -0.2121 0.2601 305.371

190 0.0462 0.3911 0.3938 83.2567 0.3427 -0.0383 0.3449 353.6187 0.1334 -0.1576 0.2064 310.245

195 0.1051 0.3867 0.4008 74.7935 0.2686 -0.0324 0.2705 353.1226 0.1225 -0.1279 0.1771 313.7603

200 0.127 0.3737 0.3947 71.2293 0.2263 -0.0292 0.2281 352.6505 0.1148 -0.1084 0.1579 316.6499

205 0.1327 0.3582 0.382 69.6735 0.199 -0.0274 0.2009 352.1657 0.109 -0.094 0.1439 319.2154

210 0.1303 0.3421 0.3661 69.1442 0.1796 -0.0264 0.1816 351.6533 0.1041 -0.0825 0.1329 321.5987

215 0.135 0.3212 0.3484 67.1989 0.147 -0.0225 0.1488 351.3031 0.0936 -0.0671 0.1152 324.3449

220 0.1246 0.3048 0.3293 67.7658 0.1361 -0.0222 0.1379 350.7293 0.0895 -0.0591 0.1073 326.5619

225 0.1132 0.2885 0.3099 68.5752 0.1264 -0.022 0.1283 350.1031 0.0856 -0.052 0.1001 328.7455

230 0.1015 0.2722 0.2906 69.5463 0.117 -0.0219 0.1191 349.3989 0.0816 -0.0454 0.0934 330.9195

235 0.0901 0.2561 0.2715 70.62 0.1077 -0.0218 0.1099 348.5799 0.0774 -0.0392 0.0867 333.1114

240 0.0792 0.2401 0.2528 71.7509 0.0981 -0.0216 0.1004 347.5945 0.0727 -0.0334 0.08 335.3607

245 0.0689 0.2241 0.2345 72.9041 0.0881 -0.0214 0.0906 346.3684 0.0676 -0.0277 0.0731 337.7306

250 0.0595 0.2081 0.2165 74.053 0.0775 -0.0211 0.0803 344.7903 0.0619 -0.0221 0.0658 340.3276

255 0.0508 0.1921 0.1987 75.1792 0.0665 -0.0207 0.0697 342.6846 0.0555 -0.0166 0.058 343.3398

260 0.043 0.1759 0.1811 76.2721 0.0551 -0.0203 0.0587 339.7526 0.0483 -0.0111 0.0496 347.1223

265 0.0351 0.1616 0.1654 77.7571 0.0453 -0.0209 0.0499 335.1936 0.0422 -0.0064 0.0427 351.3049

270 0.0288 0.1436 0.1465 78.6646 0.0324 -0.0199 0.038 328.4063 0.0327 -0.0003 0.0327 359.5214

275 0.0222 0.1207 0.1227 79.5758 0.0181 -0.018 0.0255 315.2795 0.0243 0.0091 0.0259 20.599

280 0.0165 0.0993 0.1007 80.5687 0.005 -0.0162 0.0169 287.269 0.013 0.0159 0.0206 50.6517

285 0.0109 0.0751 0.0759 81.7758 -0.0082 -0.0137 0.016 239.1562 0.0009 0.0232 0.0232 87.6968

290 0.0051 0.0471 0.0473 83.7672 -0.0216 -0.0103 0.0239 205.5305 -0.0121 0.0311 0.0334 111.2357

295 -0.0008 0.0137 0.0137 93.5491 -0.0352 -0.0055 0.0356 188.9181 -0.0261 0.04 0.0477 123.1437

300 -0.0074 -0.0269 0.0279 254.7088 -0.0491 0.0012 0.0491 178.647 -0.0411 0.0499 0.0647 129.4634

305 -0.0148 -0.0772 0.0786 259.1665 -0.0632 0.0104 0.0641 170.6522 -0.0573 0.0615 0.0841 132.9858

310 -0.0237 -0.1408 0.1428 260.4299 -0.0776 0.0231 0.081 163.4246 -0.0749 0.0751 0.1061 134.9088

315 -0.0354 -0.2232 0.226 260.992 -0.0919 0.0404 0.1003 156.2844 -0.0943 0.0917 0.1316 135.7936

320 -0.0525 -0.3385 0.3425 261.19 -0.1066 0.0651 0.1249 148.583 -0.1161 0.1141 0.1628 135.5129

325 -0.078 -0.4935 0.4996 261.0213 -0.1169 0.0966 0.1517 140.4367 -0.142 0.1412 0.2003 135.1596

330 -0.1226 -0.7317 0.7419 260.4857 -0.1195 0.1401 0.1842 130.4715 -0.1745 0.1793 0.2502 134.2295

335 -0.2538 -1.318 1.3422 259.1013 -0.0791 0.2185 0.2324 109.9112 -0.2361 0.2576 0.3494 132.5134

340 -0.6009 -2.5845 2.6535 256.9114 0.1096 0.3168 0.3353 70.9179 -0.3121 0.3765 0.4891 129.6564

345 -2.7573 -8.9526 9.3676 252.8818 1.7286 0.3395 1.7616 11.1107 -0.3472 0.5985 0.6919 120.1227

350 -117.524 -241.7038 268.7613 244.0695 118.1369 -38.1502 124.1441 342.1031 28.2671 -25.2593 37.9086 318.2163

355 -1.6132 -1.3049 2.0749 218.9677 2.0701 -1.2248 2.4053 329.3891 0.8905 -1.0429 1.3714 310.4935

360 -0.3603 0.2109 0.4175 149.6614 0.4863 -0.3796 0.6169 322.0247 0.2828 -0.3877 0.4798 306.1117

Appendix A10


theta2

degree

F32x

/10.^6

N

F32y

/10.^6

N

F32

/10.^6

N

theta32

degree

F43x

/10.^6

N

F43y

/10.^6

N

F43

/10.^6

N

theta43

degree

F53x

/10.^6

N

F53y

/10.^6

N

F53

/10.^6

N

theta53

degree

F65x

/10.^6

N

F65y

/10.^6

N

F65

/10.^6

N

theta65

degree

T/10.^3

N.m

0 0.3264 -0.2109 0.3886 327.136 0.3921 0.2557 0.4681 33.1146 -0.3303 -0.6742 0.7507 243.902 0.3269 -0.1174 0.3474 340.244 64.1659

5 0.1746 -0.2247 0.2846 307.851 0.2156 0.1236 0.2485 29.8168 -0.2121 -0.4536 0.5008 244.946 0.1985 -0.0834 0.2153 337.194 72.7438

10 0.1279 -0.1752 0.2169 306.13 0.1466 0.0881 0.171 30.9896 -0.1519 -0.333 0.3661 245.481 0.1404 -0.0586 0.1521 337.357 59.2622

15 0.1132 -0.126 0.1693 311.946 0.1148 0.078 0.1388 34.2021 -0.1144 -0.2591 0.2832 246.172 0.1127 -0.0389 0.1192 340.952 45.9358

20 0.1053 -0.0983 0.144 316.987 0.1001 0.072 0.1233 35.7168 -0.0943 -0.2193 0.2387 246.729 0.0965 -0.0295 0.1009 343.018 39.061

25 0.0982 -0.0871 0.1313 318.425 0.0936 0.0664 0.1147 35.3582 -0.0851 -0.2008 0.2181 247.041 0.0877 -0.0256 0.0914 343.764 36.6645

30 0.0887 -0.09 0.1264 314.57 0.0913 0.0602 0.1094 33.4193 -0.0843 -0.198 0.2152 246.952 0.0834 -0.0261 0.0873 342.608 37.2194

35 0.0756 -0.1038 0.1284 306.049 0.0912 0.0537 0.1058 30.4672 -0.0902 -0.207 0.2258 246.461 0.0815 -0.0301 0.0869 339.701 39.0716

40 0.0564 -0.1298 0.1415 293.484 0.0925 0.0461 0.1033 26.4757 -0.104 -0.2278 0.2504 245.466 0.0784 -0.0398 0.088 333.073 41.2861

45 0.0366 -0.1564 0.1606 283.169 0.0944 0.0402 0.1026 23.0694 -0.1193 -0.2512 0.2781 244.602 0.0787 -0.0479 0.0921 328.68 41.5187

50 0.0146 -0.1857 0.1862 274.491 0.0968 0.0352 0.103 19.9587 -0.1373 -0.2782 0.3102 243.728 0.0792 -0.0566 0.0974 324.465 39.7134

55 -0.0087 -0.2157 0.2159 267.686 0.0995 0.031 0.1042 17.3053 -0.157 -0.3068 0.3446 242.904 0.08 -0.0653 0.1033 320.752 35.4806

60 -0.0325 -0.2451 0.2472 262.457 0.1023 0.0277 0.1059 15.1564 -0.1771 -0.3354 0.3793 242.158 0.0807 -0.0736 0.1092 317.669 28.7392

65 -0.0559 -0.2727 0.2783 258.417 0.105 0.0252 0.108 13.4863 -0.1969 -0.3626 0.4126 241.498 0.0815 -0.0809 0.1148 315.222 19.6517

70 -0.0784 -0.2976 0.3078 255.243 0.1076 0.0233 0.1101 12.235 -0.2155 -0.3876 0.4434 240.925 0.0822 -0.0871 0.1197 313.354 8.557

75 -0.0995 -0.3194 0.3346 252.697 0.1099 0.022 0.1121 11.3333 -0.2323 -0.4095 0.4708 240.433 0.0829 -0.0921 0.1239 311.987 -4.0906

80 -0.1161 -0.3293 0.3492 250.585 0.1102 0.025 0.113 12.7668 -0.2423 -0.4232 0.4877 240.201 0.0831 -0.0959 0.1269 310.896 -17.3801

85 -0.1335 -0.3434 0.3685 248.758 0.1112 0.0253 0.114 12.7978 -0.2541 -0.4381 0.5065 239.887 0.0837 -0.0989 0.1295 310.237 -31.3624

90 -0.149 -0.3542 0.3843 247.187 0.1114 0.0257 0.1144 13.004 -0.2633 -0.4494 0.5209 239.639 0.0842 -0.1008 0.1314 309.867 -45.3378

95 -0.1624 -0.3616 0.3964 245.815 0.1109 0.0263 0.114 13.3413 -0.2697 -0.457 0.5306 239.455 0.0847 -0.1019 0.1325 309.733 -58.8245

100 -0.1737 -0.3657 0.4049 244.596 0.1096 0.0269 0.1129 13.7777 -0.2732 -0.4607 0.5356 239.331 0.085 -0.102 0.1327 309.792 -71.3761

105 -0.1828 -0.3665 0.4096 243.497 0.1075 0.0274 0.1109 14.2902 -0.2739 -0.4606 0.5359 239.264 0.0851 -0.1013 0.1323 310.011 -82.5882

110 -0.1896 -0.3641 0.4105 242.495 0.1045 0.0277 0.1081 14.8641 -0.2716 -0.4566 0.5312 239.254 0.0849 -0.0999 0.1311 310.361 -92.0981

115 -0.1958 -0.3589 0.4088 241.385 0.1018 0.0262 0.1051 14.4567 -0.2692 -0.4475 0.5222 238.969 0.0826 -0.0956 0.1263 310.838 -100.15

120 -0.1978 -0.3496 0.4017 240.499 0.0977 0.0259 0.1011 14.8757 -0.2615 -0.435 0.5075 238.993 0.0813 -0.0922 0.1229 311.417 -105.318

125 -0.1969 -0.3365 0.3899 239.669 0.0931 0.0254 0.0965 15.2949 -0.2507 -0.4181 0.4875 239.059 0.0795 -0.0879 0.1186 312.117 -107.824

130 -0.1925 -0.3192 0.3728 238.9 0.0882 0.0248 0.0916 15.728 -0.2366 -0.3964 0.4617 239.173 0.0771 -0.0827 0.113 312.977 -107.317

135 -0.1837 -0.2965 0.3488 238.218 0.0835 0.0243 0.0869 16.2173 -0.2188 -0.3691 0.4291 239.345 0.0739 -0.0762 0.1061 314.101 -103.324

140 -0.1685 -0.2665 0.3153 237.696 0.0795 0.0241 0.0831 16.8631 -0.1963 -0.3346 0.3879 239.605 0.0698 -0.068 0.0974 315.743 -95.0912

145 -0.1433 -0.2256 0.2672 237.578 0.0776 0.025 0.0815 17.8704 -0.1673 -0.2901 0.3349 240.033 0.0648 -0.0571 0.0864 318.573 -81.2333

150 -0.0998 -0.1657 0.1934 238.934 0.0803 0.0286 0.0853 19.5822 -0.1278 -0.2297 0.2629 240.902 0.0588 -0.0416 0.072 324.71 -58.8455

155 -0.0172 -0.0675 0.0697 255.694 0.0946 0.0389 0.1023 22.3301 -0.0684 -0.1393 0.1552 243.86 0.0526 -0.0163 0.055 342.767 -20.8312

160 0.1727 0.1281 0.215 36.5614 0.1434 0.0694 0.1593 25.8182 0.0398 0.0219 0.0454 28.7668 0.0505 0.0348 0.0613 34.5365 54.5965

165 1.0314 0.8989 1.3682 41.0731 0.4195 0.2461 0.4864 30.3926 0.4178 0.5589 0.6978 53.216 0.1052 0.2374 0.2597 66.1041 345.453

170 11.6136 8.6993 14.511 36.8354 4.3763 2.5841 5.0823 30.5611 3.8287 5.0069 6.303 52.5956 1.5719 2.4853 2.9407 57.6885 3220.7

175 8.398 3.9589 9.2844 25.2395 3.8423 2.0639 4.3616 28.2427 1.1213 0.7076 1.3259 32.2525 2.271 1.4597 2.6996 32.7323 1422.8

180 0.786 -0.1286 0.7964 350.71 0.5497 0.2471 0.6027 24.2076 -0.2419 -0.5723 0.6213 247.084 0.4774 0.0666 0.4821 7.9466 -39.1226

185 0.1529 -0.3571 0.3885 293.173 0.2382 0.0817 0.2518 18.942 -0.2708 -0.53 0.5952 242.938 0.2732 -0.031 0.275 353.534 -112.311

190 -0.0129 -0.3852 0.3854 268.088 0.1442 0.032 0.1477 12.5019 -0.2522 -0.4716 0.5348 241.866 0.2012 -0.0517 0.2077 345.575 -114.765

195 -0.0724 -0.378 0.3848 259.16 0.1029 0.0095 0.1033 5.2956 -0.2302 -0.4224 0.4811 241.407 0.1641 -0.0564 0.1735 341.02 -105.392

200 -0.0951 -0.3621 0.3744 255.278 0.0811 -0.0028 0.0812 357.994 -0.2101 -0.3813 0.4354 241.141 0.1406 -0.0562 0.1514 338.205 -93.633

205 -0.102 -0.3439 0.3587 253.484 0.0685 -0.0104 0.0693 351.374 -0.1923 -0.346 0.3958 240.941 0.1237 -0.0542 0.1351 336.326 -81.7273

210 -0.101 -0.3252 0.3405 252.748 0.0607 -0.0152 0.0626 345.945 -0.1762 -0.3147 0.3607 240.753 0.1103 -0.0515 0.1217 334.96 -70.325

215 -0.1073 -0.3018 0.3203 250.433 0.0432 -0.0237 0.0493 331.248 -0.154 -0.2721 0.3127 240.5 0.0905 -0.0482 0.1025 331.991 -56.4983

220 -0.0986 -0.283 0.2997 250.787 0.0401 -0.0253 0.0474 327.787 -0.1407 -0.2463 0.2836 240.256 0.0809 -0.0449 0.0926 330.97 -46.6751

225 -0.0892 -0.2645 0.2791 251.36 0.0375 -0.026 0.0457 325.251 -0.1284 -0.2221 0.2566 239.959 0.0721 -0.0417 0.0833 329.927 -37.7134

230 -0.0797 -0.2463 0.2589 252.058 0.0349 -0.0263 0.0437 323.028 -0.1169 -0.1992 0.231 239.592 0.0637 -0.0387 0.0745 328.743 -29.5826

235 -0.0706 -0.2284 0.239 252.809 0.0318 -0.0262 0.0413 320.498 -0.1059 -0.1772 0.2065 239.13 0.0555 -0.0357 0.066 327.283 -22.2459

240 -0.0622 -0.2107 0.2197 253.552 0.0281 -0.0262 0.0384 316.98 -0.0954 -0.1559 0.1828 238.539 0.0474 -0.0327 0.0576 325.364 -15.6663

245 -0.0546 -0.1934 0.2009 254.234 0.0234 -0.0263 0.0353 311.656 -0.0851 -0.1349 0.1595 237.764 0.0392 -0.0299 0.0493 322.701 -9.8112

250 -0.0479 -0.1763 0.1827 254.805 0.0178 -0.0268 0.0322 303.536 -0.0749 -0.1141 0.1365 236.711 0.0308 -0.027 0.041 318.792 -4.656

255 -0.0421 -0.1594 0.1648 255.216 0.0111 -0.0278 0.0299 291.716 -0.0648 -0.0932 0.1135 235.206 0.0222 -0.0241 0.0328 312.653 -0.1892

260 -0.0371 -0.1425 0.1473 255.414 0.0033 -0.0293 0.0295 276.37 -0.0546 -0.0721 0.0904 232.878 0.0133 -0.0211 0.025 302.124 3.5825

265 -0.0321 -0.1278 0.1318 255.899 -0.0036 -0.0308 0.031 263.284 -0.0459 -0.054 0.0709 229.609 0.0058 -0.0185 0.0194 287.311 6.3449

270 -0.0288 -0.1097 0.1134 255.297 -0.0142 -0.0335 0.0364 247.046 -0.0346 -0.0306 0.0462 221.44 -0.0045 -0.0151 0.0157 253.526 8.7613

275 -0.0252 -0.0869 0.0905 253.856 -0.0268 -0.0356 0.0446 233.049 -0.0211 -0.0033 0.0213 188.828 -0.0132 -0.0084 0.0156 212.417 9.9314

280 -0.0224 -0.0659 0.0696 251.247 -0.039 -0.0382 0.0546 224.374 -0.0089 0.0223 0.024 111.8 -0.0242 -0.0042 0.0246 189.85 10.1923

285 -0.0196 -0.0424 0.0467 245.147 -0.0521 -0.0402 0.0658 217.65 0.004 0.0495 0.0496 85.4278 -0.0356 0.0005 0.0356 179.135 9.1099

290 -0.0167 -0.0152 0.0226 222.247 -0.066 -0.0411 0.0777 211.911 0.0177 0.0787 0.0807 77.3088 -0.0476 0.006 0.048 172.784 6.3672

295 -0.0135 0.0171 0.0217 128.315 -0.0808 -0.0402 0.0902 206.472 0.0327 0.1108 0.1155 73.5577 -0.0601 0.0125 0.0614 168.26 1.5238

300 -0.0096 0.0563 0.0571 99.6813 -0.0966 -0.0367 0.1033 200.828 0.0493 0.1466 0.1546 71.4272 -0.0734 0.0202 0.0761 164.568 -6.0305

305 -0.0047 0.1049 0.105 92.5526 -0.1135 -0.0295 0.1173 194.572 0.0679 0.1873 0.1992 70.0691 -0.0875 0.0297 0.0924 161.242 -17.1501

310 0.0019 0.1667 0.1667 89.3333 -0.1319 -0.017 0.133 187.367 0.0895 0.2349 0.2514 69.14 -0.103 0.0415 0.111 158.03 -33.0656

315 0.0114 0.2472 0.2474 87.3569 -0.1518 0.0028 0.1518 178.934 0.1153 0.2924 0.3144 68.4756 -0.1202 0.0566 0.1329 154.771 -55.6402

320 0.0265 0.3603 0.3612 85.795 -0.1751 0.035 0.1786 168.711 0.1495 0.3683 0.3975 67.903 -0.1401 0.078 0.1603 150.885 -89.1616

325 0.0502 0.513 0.5154 84.4102 -0.1994 0.0827 0.2158 157.475 0.1918 0.4648 0.5028 67.578 -0.1644 0.1055 0.1954 147.301 -136.625

330 0.0933 0.7487 0.7544 82.8983 -0.2269 0.1616 0.2786 144.547 0.2527 0.606 0.6566 67.3597 -0.1964 0.1472 0.2454 143.157 -211.487

335 0.223 1.3323 1.3509 80.4961 -0.2649 0.3698 0.4548 125.615 0.389 0.9331 1.011 67.3689 -0.2615 0.2465 0.3593 136.697 -396.128

340 0.569 2.5961 2.6577 77.6369 -0.2733 0.8633 0.9055 107.568 0.6442 1.5618 1.6894 67.5859 -0.349 0.4501 0.5696 127.789 -801.579

345 2.7246 8.9614 9.3664 73.0891 0.1688 3.6735 3.6774 87.3685 1.63 4.1446 4.4536 68.5309 -0.4427 1.3812 1.4505 107.771 -2848.6

350 117.491 241.71 268.75 64.0765 59.2783 136.871 149.156 66.5827 10.3059 44.5409 45.7177 76.9722 27.5339 27.1432 38.6636 44.5906 -78643

355 1.5794 1.3078 2.0506 39.6254 1.3824 1.5489 2.0761 48.2513 -0.6701 -1.1758 1.3534 240.319 0.9484 -0.0702 0.951 355.767 -438.34

360 0.3264 -0.2109 0.3886 327.136 0.3921 0.2557 0.4681 33.1146 -0.3303 -0.6742 0.7507 243.902 0.3269 -0.1174 0.3474 340.244 64.1659

Appendix A11


theta2

degree

F12x

/10.^6

N

F12y

/10.^6

N

F12

/10.^6

N

theta12

degree

F14x

/10.^6

N

F14y

/10.^6

N

F14

/10.^6

N

theta14

degree

F16x

/10.^6

N

F16y

/10.^6

N

F16

/10.^6

N

theta16

degree

0 -0.3499 0.2159 0.4111 148.3297 0.4772 -0.3746 0.6067 321.8714 0.2815 -0.3997 0.4889 305.1535

5 -0.2019 0.2275 0.3042 131.5868 0.2336 -0.1996 0.3073 319.4953 0.1561 -0.2507 0.2953 301.9148

10 -0.1561 0.1751 0.2345 131.7217 0.1421 -0.1198 0.1858 319.8497 0.098 -0.1796 0.2046 298.616

15 -0.1412 0.1229 0.1872 138.9708 0.0997 -0.0752 0.1249 322.9739 0.0691 -0.1373 0.1537 296.6966

20 -0.1327 0.0924 0.1617 145.1585 0.0789 -0.0521 0.0946 326.568 0.0513 -0.1153 0.1262 293.9909

25 -0.1246 0.0784 0.1472 147.8153 0.0683 -0.041 0.0797 329.0117 0.041 -0.1035 0.1113 291.6175

30 -0.1138 0.0785 0.1382 145.4068 0.0631 -0.0375 0.0734 329.2723 0.0353 -0.0987 0.1048 289.6804

35 -0.0992 0.0894 0.1336 137.9555 0.0609 -0.0385 0.072 327.6998 0.0324 -0.0986 0.1037 288.2066

40 -0.0784 0.1127 0.1373 124.8322 0.0605 -0.0429 0.0742 324.6125 0.0288 -0.1048 0.1087 285.3781

45 -0.0568 0.1366 0.148 112.5909 0.0612 -0.0472 0.0773 322.3468 0.0289 -0.1096 0.1133 284.7518

50 -0.0329 0.1634 0.1667 101.3972 0.0627 -0.0516 0.0812 320.5946 0.0296 -0.1153 0.119 284.4192

55 -0.0076 0.1912 0.1913 92.2793 0.065 -0.0555 0.0855 319.5024 0.0309 -0.1211 0.1249 284.3189

60 0.0183 0.2185 0.2192 85.2143 0.0677 -0.0587 0.0896 319.043 0.0325 -0.1263 0.1304 284.4112

65 0.044 0.2442 0.2481 79.7846 0.0707 -0.0612 0.0935 319.1204 0.0342 -0.1308 0.1352 284.6701

70 0.0689 0.2676 0.2763 75.5583 0.0738 -0.0627 0.0968 319.6257 0.0361 -0.1341 0.1389 285.0774

75 0.0925 0.2881 0.3026 72.1981 0.0768 -0.0634 0.0996 320.4616 0.0381 -0.1363 0.1415 285.6195

80 0.1116 0.2971 0.3173 69.4042 0.0775 -0.0585 0.0971 322.9503 0.0399 -0.1373 0.1429 286.2022

85 0.1317 0.3105 0.3373 67.0167 0.0796 -0.0567 0.0977 324.5127 0.042 -0.1375 0.1438 286.9817

90 0.1498 0.3209 0.3541 64.97 0.0812 -0.0543 0.0977 326.2204 0.0441 -0.1368 0.1438 287.8679

95 0.1659 0.3282 0.3677 63.1812 0.0821 -0.0513 0.0968 328.0318 0.0462 -0.1352 0.1429 288.8517

100 0.1798 0.3324 0.3779 61.5901 0.0824 -0.0477 0.0953 329.9171 0.0481 -0.1328 0.1412 289.9248

105 0.1915 0.3337 0.3847 60.1517 0.0819 -0.0438 0.0929 331.8572 0.0499 -0.1296 0.1388 291.0788

110 0.2008 0.332 0.388 58.8321 0.0806 -0.0396 0.0898 333.8425 0.0515 -0.1256 0.1358 292.3047

115 0.2094 0.3278 0.389 57.4245 0.0794 -0.0368 0.0875 335.1457 0.0511 -0.1188 0.1293 293.2755

120 0.2137 0.3197 0.3846 56.2422 0.0765 -0.0324 0.0831 337.0458 0.0516 -0.1131 0.1244 294.5309

125 0.2149 0.3082 0.3757 55.1096 0.0728 -0.028 0.078 338.9799 0.0516 -0.1068 0.1186 295.7933

130 0.2125 0.2926 0.3616 54.0113 0.0682 -0.0235 0.0722 340.9872 0.0508 -0.0997 0.1119 297.0226

135 0.2054 0.2718 0.3407 52.9324 0.0629 -0.0191 0.0657 343.1498 0.0491 -0.0918 0.1041 298.1451

140 0.1917 0.2441 0.3103 51.8579 0.057 -0.0146 0.0589 345.6374 0.046 -0.083 0.0949 299.0093

145 0.1678 0.2055 0.2653 50.7751 0.051 -0.0101 0.052 348.8049 0.041 -0.0731 0.0838 299.2525

150 0.1258 0.1483 0.1945 49.7035 0.0461 -0.0054 0.0464 353.334 0.0326 -0.0618 0.0699 297.8163

155 0.0457 0.0533 0.0702 49.3891 0.046 -0.0001 0.046 359.854 0.0183 -0.0489 0.0522 290.5064

160 -0.1369 -0.1382 0.1945 225.2804 0.0656 0.0065 0.0659 5.6255 -0.0096 -0.0353 0.0366 254.7615

165 -0.9479 -0.8986 1.3062 223.4711 0.2523 0.0214 0.2532 4.8596 -0.1 -0.0425 0.1086 203.0488

170 -10.6714 -8.583 13.6947 218.8096 3.7395 -0.0269 3.7396 359.5884 -0.7389 -0.8698 1.1413 229.6524

175 -7.2967 -3.8431 8.2469 207.7753 4.4183 -0.3143 4.4295 355.9309 0.2106 -1.6344 1.6479 277.3438

180 -0.571 0.1461 0.5894 165.6467 0.7903 -0.0849 0.7948 353.8708 0.1912 -0.3771 0.4228 296.8885

185 -0.0319 0.3676 0.369 94.9525 0.4066 -0.0522 0.4099 352.6844 0.1565 -0.2201 0.2701 305.4178

190 0.1024 0.3956 0.4086 75.4918 0.2819 -0.0402 0.2847 351.8818 0.1381 -0.1622 0.213 310.417

195 0.146 0.3897 0.4161 69.4634 0.2236 -0.0343 0.2262 351.2687 0.1266 -0.131 0.1821 314.0329

200 0.1586 0.3757 0.4078 67.1112 0.1909 -0.0311 0.1935 350.75 0.1185 -0.1105 0.1621 317.0003

205 0.1579 0.3595 0.3926 66.289 0.1704 -0.0292 0.1729 350.2824 0.1124 -0.0955 0.1475 319.6257

210 0.1507 0.3428 0.3744 66.2706 0.1562 -0.028 0.1587 349.8423 0.1072 -0.0836 0.136 322.0545

215 0.1505 0.3212 0.3547 64.9044 0.1289 -0.024 0.1311 349.4639 0.0963 -0.0677 0.1178 324.8821

220 0.1371 0.3043 0.3338 65.7535 0.1211 -0.0234 0.1234 349.0482 0.0921 -0.0595 0.1096 327.1256

225 0.1232 0.2875 0.3128 66.8061 0.114 -0.023 0.1163 348.6032 0.0879 -0.0521 0.1022 329.327

230 0.1095 0.2709 0.2922 67.9935 0.107 -0.0226 0.1093 348.0917 0.0837 -0.0454 0.0952 331.5124

235 0.0963 0.2544 0.272 69.263 0.0996 -0.0221 0.102 347.4688 0.0792 -0.0391 0.0884 333.7118

240 0.0839 0.238 0.2523 70.5722 0.0916 -0.0217 0.0942 346.6776 0.0744 -0.0332 0.0815 335.968

245 0.0725 0.2217 0.2332 71.887 0.083 -0.0212 0.0856 345.642 0.0691 -0.0274 0.0744 338.3477

250 0.0621 0.2055 0.2146 73.1803 0.0736 -0.0208 0.0765 344.2519 0.0632 -0.0218 0.0669 340.9619

255 0.0527 0.1892 0.1964 74.432 0.0635 -0.0202 0.0666 342.336 0.0567 -0.0162 0.059 344.0047

260 0.0443 0.1727 0.1783 75.6289 0.0528 -0.0196 0.0563 339.6031 0.0493 -0.0106 0.0505 347.8385

265 0.036 0.1583 0.1623 77.1987 0.0435 -0.0201 0.0479 335.2344 0.043 -0.006 0.0434 352.0677

270 0.0294 0.1401 0.1431 78.156 0.031 -0.0189 0.0363 328.6583 0.0335 0.0002 0.0335 0.3965

275 0.0226 0.1169 0.1191 79.061 0.0171 -0.0168 0.024 315.5229 0.0249 0.0097 0.0267 21.2339

280 0.0168 0.0953 0.0967 79.9996 0.0042 -0.0148 0.0154 285.679 0.0136 0.0165 0.0214 50.5293

285 0.0112 0.0708 0.0717 81.0403 -0.009 -0.0121 0.0151 233.4066 0.0014 0.0239 0.0239 86.5515

290 0.0055 0.0424 0.0427 82.5803 -0.0224 -0.0084 0.0239 200.6031 -0.0116 0.0319 0.034 110.0415

295 -0.0003 0.0085 0.0085 92.2315 -0.0361 -0.0033 0.0363 185.2073 -0.0257 0.0408 0.0482 122.1587

300 -0.0066 -0.0326 0.0332 258.4634 -0.0502 0.0038 0.0503 175.6493 -0.0407 0.0509 0.0652 128.6481

305 -0.0138 -0.0835 0.0846 260.598 -0.0646 0.0136 0.066 168.1097 -0.0569 0.0625 0.0845 132.2891

310 -0.0225 -0.1478 0.1495 261.3437 -0.0793 0.027 0.0837 161.2211 -0.0745 0.0763 0.1066 134.297

315 -0.0338 -0.2312 0.2337 261.6749 -0.0939 0.045 0.1041 154.3716 -0.0938 0.093 0.1321 135.2461

320 -0.0505 -0.3477 0.3514 261.7318 -0.1091 0.0709 0.1301 146.9828 -0.1156 0.1155 0.1634 135.0179

325 -0.0756 -0.5044 0.51 261.4811 -0.1201 0.1039 0.1588 139.1232 -0.1413 0.1428 0.2009 134.7086

330 -0.1194 -0.7451 0.7546 260.892 -0.1237 0.1498 0.1943 129.5448 -0.1736 0.1809 0.2507 133.8196

335 -0.2484 -1.3381 1.3609 259.4825 -0.0863 0.2352 0.2505 110.1386 -0.2344 0.2589 0.3492 132.1578

340 -0.5894 -2.6184 2.6839 257.3138 0.0945 0.3495 0.362 74.8659 -0.3085 0.3758 0.4862 129.3876

345 -2.7051 -9.0567 9.4521 253.3698 1.6627 0.4635 1.7261 15.5763 -0.3335 0.5765 0.666 120.0533

350 -115.1099 -244.2687 270.0324 244.7682 115.32 -33.7897 120.1684 343.669 28.6699 -27.057 39.4213 316.6578

355 -1.575 -1.317 2.0531 219.9022 2.0302 -1.1772 2.3468 329.8937 0.8922 -1.0804 1.4012 309.5506

360 -0.3499 0.2159 0.4111 148.3297 0.4772 -0.3746 0.6067 321.8714 0.2815 -0.3997 0.4889 305.1535

Appendix A11


theta2

degree

F32x

/10.^6

N

F32y

/10.^6

N

F32

/10.^6

N

theta32

degree

F43x

/10.^6

N

F43y

/10.^6

N

F43

/10.^6

N

theta43

degree

F53x

/10.^6

N

F53y

/10.^6

N

F53

/10.^6

N

theta53

degree

F65x

/10.^6

N

F65y

/10.^6

N

F65

/10.^6

N

theta65

degree

T/10.^3

N.m

0 0.316 -0.2162 0.3829 325.618 0.383 0.2613 0.4637 34.296 -0.3316 -0.6857 0.7617 244.194 0.3256 -0.1291 0.3503 338.365 65.7076

5 0.1681 -0.2308 0.2856 306.067 0.2107 0.1242 0.2446 30.5248 -0.2136 -0.4611 0.5082 245.141 0.1969 -0.0911 0.2169 335.167 74.3431

10 0.1227 -0.1813 0.2189 304.087 0.1431 0.087 0.1675 31.3079 -0.1536 -0.3388 0.372 245.611 0.1387 -0.0645 0.153 335.063 60.7288

15 0.1085 -0.1321 0.1709 309.406 0.1119 0.0762 0.1354 34.2589 -0.1162 -0.264 0.2884 246.245 0.1109 -0.044 0.1193 338.357 47.2689

20 0.1008 -0.1043 0.1451 314.022 0.0974 0.0697 0.1198 35.5856 -0.0961 -0.2237 0.2435 246.748 0.0946 -0.0341 0.1006 340.181 40.2405

25 0.0938 -0.0931 0.1322 315.227 0.091 0.0639 0.1112 35.0804 -0.0869 -0.205 0.2226 247.015 0.0859 -0.0299 0.0909 340.804 37.6589

30 0.0844 -0.0958 0.1277 311.384 0.0889 0.0577 0.106 33.0156 -0.0861 -0.2019 0.2195 246.898 0.0815 -0.0302 0.0869 339.651 38.0004

35 0.0714 -0.1093 0.1305 303.168 0.0889 0.0513 0.1027 29.9589 -0.092 -0.2107 0.2299 246.398 0.0796 -0.034 0.0865 336.862 39.6245

40 0.0524 -0.1348 0.1447 291.248 0.0904 0.0438 0.1004 25.8749 -0.1058 -0.2312 0.2542 245.412 0.0766 -0.0435 0.0881 330.423 41.6129

45 0.0329 -0.161 0.1643 281.54 0.0924 0.0382 0.1 22.4368 -0.121 -0.2544 0.2817 244.556 0.0769 -0.0512 0.0924 326.322 41.6368

50 0.0111 -0.1897 0.1901 273.362 0.095 0.0333 0.1007 19.3324 -0.139 -0.2811 0.3136 243.692 0.0776 -0.0597 0.0979 322.42 39.6521

55 -0.0118 -0.2193 0.2196 266.911 0.0979 0.0294 0.1022 16.7146 -0.1585 -0.3094 0.3477 242.877 0.0784 -0.0682 0.1039 319.008 35.276

60 -0.0352 -0.2482 0.2507 261.919 0.1009 0.0263 0.1042 14.619 -0.1785 -0.3377 0.382 242.138 0.0794 -0.0761 0.1099 316.196 28.4301

65 -0.0583 -0.2753 0.2814 258.036 0.1038 0.024 0.1066 13.0099 -0.1981 -0.3647 0.415 241.484 0.0803 -0.0831 0.1156 313.985 19.2764

70 -0.0805 -0.2998 0.3104 254.97 0.1066 0.0223 0.1089 11.8191 -0.2166 -0.3894 0.4456 240.916 0.0811 -0.0891 0.1205 312.318 8.1509

75 -0.1013 -0.3212 0.3368 252.5 0.109 0.0211 0.111 10.9729 -0.2332 -0.4111 0.4726 240.429 0.0819 -0.0938 0.1246 311.122 -4.4961

80 -0.1175 -0.3308 0.3511 250.443 0.1096 0.0242 0.1122 12.4517 -0.2431 -0.4245 0.4892 240.2 0.0823 -0.0975 0.1275 310.169 -17.7528

85 -0.1346 -0.3446 0.37 248.66 0.1107 0.0246 0.1134 12.5187 -0.2547 -0.4393 0.5078 239.889 0.083 -0.1002 0.1302 309.636 -31.6845

90 -0.1498 -0.3551 0.3854 247.126 0.1111 0.0251 0.1139 12.7508 -0.2638 -0.4504 0.5219 239.645 0.0837 -0.102 0.132 309.375 -45.5916

95 -0.1629 -0.3623 0.3973 245.785 0.1108 0.0258 0.1137 13.1035 -0.27 -0.4578 0.5315 239.464 0.0843 -0.1029 0.133 309.336 -58.9961

100 -0.1739 -0.3662 0.4054 244.594 0.1096 0.0264 0.1128 13.5441 -0.2735 -0.4613 0.5363 239.342 0.0847 -0.1028 0.1332 309.48 -71.4553

105 -0.1827 -0.3668 0.4098 243.523 0.1077 0.0269 0.111 14.0488 -0.274 -0.4611 0.5363 239.278 0.0849 -0.102 0.1327 309.773 -82.5675

110 -0.1892 -0.3642 0.4104 242.549 0.1049 0.0273 0.1084 14.6008 -0.2716 -0.4569 0.5316 239.27 0.0849 -0.1005 0.1315 310.191 -91.9729

115 -0.1951 -0.3589 0.4085 241.47 0.1024 0.0258 0.1057 14.1597 -0.2691 -0.4477 0.5224 238.986 0.0827 -0.096 0.1267 310.732 -99.9147

120 -0.1968 -0.3495 0.401 240.621 0.0986 0.0255 0.1018 14.5242 -0.2613 -0.4351 0.5076 239.011 0.0815 -0.0925 0.1233 311.368 -104.975

125 -0.1955 -0.3363 0.389 239.836 0.0943 0.025 0.0976 14.8648 -0.2505 -0.4181 0.4874 239.078 0.0797 -0.0882 0.1188 312.118 -107.376

130 -0.1907 -0.3189 0.3716 239.124 0.0898 0.0244 0.0931 15.1892 -0.2363 -0.3964 0.4615 239.192 0.0773 -0.0828 0.1133 313.024 -106.771

135 -0.1814 -0.2962 0.3473 238.518 0.0855 0.0238 0.0888 15.5347 -0.2185 -0.3689 0.4288 239.363 0.0741 -0.0762 0.1063 314.185 -102.693

140 -0.1657 -0.2662 0.3136 238.104 0.0821 0.0235 0.0854 16.0019 -0.196 -0.3344 0.3876 239.62 0.07 -0.068 0.0976 315.846 -94.4003

145 -0.14 -0.2254 0.2653 238.149 0.0807 0.0244 0.0843 16.8182 -0.1671 -0.2899 0.3346 240.042 0.0649 -0.0571 0.0865 318.658 -80.5331

150 -0.0964 -0.1657 0.1917 239.8 0.0837 0.0279 0.0882 18.4192 -0.1278 -0.2296 0.2628 240.901 0.0588 -0.0417 0.0721 324.665 -58.2426

155 -0.0149 -0.068 0.0696 257.601 0.0971 0.0381 0.1043 21.4154 -0.0686 -0.1396 0.1556 243.844 0.0524 -0.0168 0.055 342.196 -20.58

160 0.1687 0.1262 0.2107 36.8048 0.1401 0.0686 0.156 26.0792 0.0391 0.0202 0.0441 27.3052 0.0499 0.0329 0.0597 33.4293 53.7501

165 0.9807 0.8895 1.324 42.2087 0.3705 0.2454 0.4444 33.524 0.4161 0.5494 0.6892 52.8603 0.1035 0.2278 0.2502 65.5674 338.778

170 10.7048 8.5767 13.717 38.7018 3.4644 2.5903 4.3257 36.7849 3.8316 4.8774 6.2025 51.8474 1.5748 2.3557 2.8336 56.2361 3136

175 7.3305 3.8398 8.2752 27.646 2.7439 2.07 3.4371 37.0308 1.1522 0.5818 1.2908 26.7903 2.3018 1.3337 2.6603 30.0888 1358.5

180 0.6049 -0.1465 0.6224 346.387 0.3597 0.2467 0.4362 34.4464 -0.2329 -0.5904 0.6347 248.469 0.4864 0.0483 0.4888 5.6702 -44.4845

185 0.0656 -0.3651 0.3709 280.192 0.145 0.0806 0.1659 29.0681 -0.2649 -0.5375 0.5992 243.767 0.2791 -0.0386 0.2818 352.125 -112.312

190 -0.069 -0.3901 0.3961 259.972 0.0834 0.0306 0.0888 20.166 -0.2474 -0.4757 0.5362 242.521 0.2059 -0.056 0.2134 344.775 -113.153

195 -0.1132 -0.3813 0.3977 253.46 0.0579 0.0081 0.0585 7.963 -0.2261 -0.4249 0.4813 241.981 0.1682 -0.0591 0.1783 340.623 -103.059

200 -0.1267 -0.3644 0.3859 250.824 0.0458 -0.0042 0.046 354.704 -0.2064 -0.3829 0.435 241.67 0.1443 -0.058 0.1555 338.094 -90.9329

205 -0.1272 -0.3455 0.3682 249.796 0.04 -0.0117 0.0416 343.691 -0.1889 -0.347 0.3951 241.439 0.1271 -0.0554 0.1386 336.434 -78.8577

210 -0.1213 -0.3262 0.348 249.599 0.0373 -0.0163 0.0407 336.353 -0.1731 -0.3153 0.3597 241.229 0.1134 -0.0523 0.1249 335.249 -67.4222

215 -0.1227 -0.3022 0.3261 247.903 0.025 -0.0247 0.0351 315.412 -0.1512 -0.2722 0.3114 240.946 0.0933 -0.0484 0.1051 332.558 -53.8322

220 -0.1111 -0.2829 0.3039 248.561 0.0251 -0.026 0.0361 314.019 -0.1382 -0.2461 0.2822 240.685 0.0835 -0.045 0.0948 331.686 -44.1439

225 -0.0992 -0.2639 0.282 249.396 0.0252 -0.0265 0.0365 313.595 -0.1261 -0.2217 0.2551 240.369 0.0744 -0.0416 0.0853 330.787 -35.3746

230 -0.0877 -0.2453 0.2605 250.329 0.0248 -0.0264 0.0362 313.245 -0.1148 -0.1987 0.2295 239.981 0.0658 -0.0384 0.0762 329.748 -27.4783

235 -0.0769 -0.227 0.2396 251.292 0.0237 -0.0261 0.0353 312.258 -0.104 -0.1766 0.205 239.495 0.0574 -0.0353 0.0674 328.445 -20.4032

240 -0.067 -0.209 0.2195 252.229 0.0216 -0.0258 0.0337 309.944 -0.0937 -0.1552 0.1813 238.876 0.0491 -0.0322 0.0587 326.706 -14.0985

245 -0.0582 -0.1913 0.2 253.085 0.0184 -0.0257 0.0316 305.511 -0.0836 -0.1341 0.158 238.069 0.0407 -0.0293 0.0501 324.266 -8.5191

250 -0.0505 -0.174 0.1812 253.81 0.0138 -0.026 0.0295 298.033 -0.0736 -0.1133 0.1351 236.978 0.0321 -0.0264 0.0416 320.656 -3.6303

255 -0.0439 -0.1568 0.1629 254.349 0.0081 -0.0268 0.028 286.741 -0.0636 -0.0923 0.1121 235.421 0.0234 -0.0234 0.0331 314.937 0.5874

260 -0.0384 -0.1397 0.1449 254.644 0.001 -0.0281 0.0281 272.008 -0.0536 -0.0711 0.089 233.016 0.0143 -0.0204 0.0249 304.981 4.1323

265 -0.033 -0.1249 0.1292 255.194 -0.0054 -0.0295 0.03 259.639 -0.0451 -0.053 0.0696 229.623 0.0066 -0.0177 0.0189 290.524 6.7021

270 -0.0294 -0.1065 0.1105 254.586 -0.0155 -0.032 0.0355 244.119 -0.0339 -0.0295 0.0449 221.072 -0.0037 -0.0142 0.0147 255.4 8.9383

275 -0.0255 -0.0835 0.0873 252.988 -0.0278 -0.0339 0.0439 230.643 -0.0204 -0.0022 0.0206 186.071 -0.0125 -0.0075 0.0146 210.836 9.9513

280 -0.0227 -0.0623 0.0663 249.98 -0.0399 -0.0363 0.054 222.303 -0.0083 0.0234 0.0249 109.589 -0.0236 -0.0032 0.0238 187.833 10.073

285 -0.0199 -0.0384 0.0433 242.578 -0.0529 -0.0381 0.0652 215.75 0.0045 0.0507 0.0509 84.97 -0.0351 0.0016 0.0352 177.462 8.8621

290 -0.0171 -0.0109 0.0203 212.436 -0.0668 -0.0387 0.0772 210.077 0.0182 0.08 0.0821 77.1958 -0.0471 0.0071 0.0477 171.406 5.9926

295 -0.014 0.0218 0.0259 122.676 -0.0817 -0.0375 0.0899 204.642 0.0331 0.1122 0.117 73.5485 -0.0597 0.0137 0.0612 167.094 1.0138

300 -0.0103 0.0615 0.0624 99.5053 -0.0977 -0.0336 0.1033 198.963 0.0497 0.1481 0.1562 71.4562 -0.0729 0.0215 0.076 163.555 -6.6957

305 -0.0056 0.1109 0.111 92.9042 -0.1149 -0.0258 0.1178 192.662 0.0683 0.1889 0.2009 70.1115 -0.0871 0.0311 0.0925 160.346 -18.0028

310 0.0007 0.1734 0.1734 89.7638 -0.1335 -0.0127 0.1341 185.427 0.09 0.2366 0.2532 69.1842 -0.1025 0.043 0.1112 157.229 -34.1514

315 0.0099 0.2548 0.255 87.7834 -0.1538 0.008 0.154 177.014 0.1158 0.2943 0.3162 68.5149 -0.1197 0.0582 0.1331 154.052 -57.0211

320 0.0246 0.3691 0.37 86.1936 -0.1776 0.0413 0.1824 166.925 0.1501 0.3703 0.3996 67.9327 -0.1395 0.0798 0.1607 150.242 -90.9266

325 0.0478 0.5235 0.5256 84.7846 -0.2025 0.0905 0.2218 155.919 0.1925 0.4669 0.505 67.5929 -0.1637 0.1074 0.1958 146.732 -138.899

330 0.0901 0.7616 0.7669 83.2545 -0.2311 0.1718 0.288 143.37 0.2537 0.6081 0.6589 67.3533 -0.1954 0.1491 0.2458 142.666 -214.501

335 0.2177 1.352 1.3694 80.8532 -0.272 0.387 0.473 125.1 0.3908 0.935 1.0133 67.3173 -0.2598 0.2481 0.3592 136.316 -400.954

340 0.5576 2.6296 2.6881 78.0288 -0.2884 0.8964 0.9417 107.835 0.6478 1.5615 1.6906 67.4694 -0.3454 0.4496 0.567 127.529 -810.056

345 2.6724 9.0651 9.4508 73.5746 0.103 3.7981 3.7995 88.4471 1.6437 4.1231 4.4387 68.2649 -0.429 1.3596 1.4256 107.512 -2875.1

350 115.077 244.274 270.02 64.7751 56.4615 141.232 152.1 68.2095 10.7086 42.7438 44.0648 75.9352 27.9367 25.3459 37.721 42.2163 -79284

355 1.5412 1.3196 2.029 40.5699 1.3425 1.597 2.0863 49.95 -0.6684 -1.2128 1.3848 241.139 0.9502 -0.1074 0.9562 353.552 -440.994

360 0.316 -0.2162 0.3829 325.618 0.383 0.2613 0.4637 34.296 -0.3316 -0.6857 0.7617 244.194 0.3256 -0.1291 0.3503 338.365 65.7076

Appendix A12


theta2

degree

F12x

/10.^6

N

F12y

/10.^6

N

F12

/10.^6

N

theta12

degree

F14x

/10.^6

N

F14y

/10.^6

N

F14

/10.^6

N

theta14

degree

F16x

/10.^6

N

F16y

/10.^6

N

F16

/10.^6

N

theta16

degree

0 -0.3608 0.2091 0.417 149.9094 0.4866 -0.3797 0.6172 322.0362 0.2829 -0.3878 0.48 306.1164

5 -0.2089 0.22 0.3034 133.5123 0.2389 -0.2 0.3115 320.0728 0.1578 -0.2428 0.2896 303.025

10 -0.1618 0.1677 0.233 133.9722 0.1459 -0.1186 0.188 320.8983 0.0998 -0.1735 0.2002 299.915

15 -0.1464 0.1156 0.1866 141.7003 0.103 -0.0732 0.1264 324.5832 0.071 -0.132 0.1499 298.2567

20 -0.1377 0.0852 0.1619 148.2442 0.0819 -0.0498 0.0958 328.7176 0.0533 -0.1104 0.1226 295.7503

25 -0.1294 0.0714 0.1478 151.1112 0.0712 -0.0386 0.081 331.5388 0.043 -0.099 0.1079 293.4975

30 -0.1185 0.0717 0.1385 148.8121 0.0658 -0.0351 0.0746 331.9487 0.0373 -0.0944 0.1015 291.5761

35 -0.1038 0.0831 0.1329 141.3229 0.0634 -0.0362 0.073 330.3197 0.0344 -0.0945 0.1006 290.0225

40 -0.0828 0.1067 0.1351 127.8058 0.0629 -0.0408 0.075 327.0163 0.0308 -0.101 0.1056 286.9628

45 -0.061 0.1311 0.1446 114.9457 0.0634 -0.0453 0.0779 324.4767 0.0308 -0.1061 0.1104 286.1774

50 -0.0368 0.1584 0.1627 103.0853 0.0648 -0.0499 0.0818 322.4345 0.0314 -0.112 0.1164 285.6821

55 -0.0112 0.1867 0.1871 93.4323 0.0669 -0.054 0.086 321.07 0.0326 -0.1181 0.1225 285.4282

60 0.015 0.2145 0.215 85.9968 0.0694 -0.0575 0.0901 320.3702 0.034 -0.1236 0.1282 285.3813

65 0.041 0.2407 0.2442 80.3238 0.0722 -0.0601 0.094 320.2422 0.0356 -0.1283 0.1332 285.5167

70 0.0663 0.2645 0.2727 75.938 0.0752 -0.0618 0.0973 320.575 0.0374 -0.1319 0.1371 285.8153

75 0.0902 0.2854 0.2993 72.4708 0.0781 -0.0626 0.1001 321.2669 0.0392 -0.1343 0.1399 286.2616

80 0.1096 0.2947 0.3144 69.6033 0.0786 -0.0578 0.0976 323.6611 0.0408 -0.1355 0.1416 286.7626

85 0.1299 0.3084 0.3347 67.1587 0.0806 -0.0562 0.0982 325.1209 0.0428 -0.136 0.1426 287.4656

90 0.1483 0.319 0.3518 65.0686 0.082 -0.0538 0.0981 326.7422 0.0448 -0.1355 0.1427 288.2829

95 0.1646 0.3266 0.3657 63.2448 0.0829 -0.0508 0.0972 328.4805 0.0467 -0.1341 0.142 289.2044

100 0.1788 0.331 0.3762 61.6234 0.083 -0.0473 0.0956 330.304 0.0485 -0.1318 0.1404 290.2205

105 0.1907 0.3325 0.3833 60.1572 0.0824 -0.0434 0.0931 332.1918 0.0502 -0.1287 0.1382 291.322

110 0.2003 0.3309 0.3868 58.8099 0.0808 -0.0392 0.0898 334.1328 0.0517 -0.1249 0.1352 292.4994

115 0.2092 0.3268 0.388 57.3727 0.0794 -0.0364 0.0874 335.3951 0.0512 -0.1182 0.1288 293.423

120 0.2138 0.3189 0.3839 56.1565 0.0764 -0.032 0.0828 337.2629 0.0517 -0.1127 0.124 294.6361

125 0.2154 0.3074 0.3753 54.9833 0.0724 -0.0275 0.0774 339.1713 0.0516 -0.1064 0.1182 295.8603

130 0.2133 0.2918 0.3615 53.8337 0.0675 -0.023 0.0713 341.1625 0.0508 -0.0994 0.1116 297.057

135 0.2066 0.2711 0.3408 52.6872 0.0617 -0.0185 0.0644 343.3271 0.049 -0.0916 0.1039 298.1568

140 0.1934 0.2433 0.3108 51.5199 0.0554 -0.014 0.0571 345.8593 0.046 -0.0829 0.0948 299.0173

145 0.1699 0.2046 0.266 50.3011 0.0489 -0.0094 0.0498 349.1768 0.0409 -0.073 0.0837 299.299

150 0.128 0.1472 0.195 48.9992 0.0438 -0.0045 0.044 354.084 0.0328 -0.0616 0.0697 298.0092

155 0.0467 0.0516 0.0696 47.8681 0.0446 0.0008 0.0446 1.0722 0.0187 -0.0482 0.0517 291.1569

160 -0.1421 -0.1413 0.2004 224.8266 0.07 0.0075 0.0704 6.0873 -0.0088 -0.0333 0.0344 255.226

165 -0.9999 -0.9093 1.3516 222.2821 0.3024 0.0223 0.3032 4.2178 -0.0981 -0.0327 0.1034 198.4483

170 -11.5815 -8.7069 14.4894 216.9354 4.6525 -0.0328 4.6526 359.5964 -0.7417 -0.74 1.0477 224.9337

175 -8.3656 -3.9635 9.257 205.3511 5.5179 -0.3201 5.5272 356.6801 0.1799 -1.5082 1.5189 276.8039

180 -0.7534 0.1268 0.764 170.4428 0.9815 -0.0841 0.9851 355.1013 0.1824 -0.3586 0.4023 296.9632

185 -0.1204 0.3583 0.378 108.5732 0.5009 -0.0507 0.5034 354.2195 0.1508 -0.2123 0.2604 305.3837

190 0.0449 0.3893 0.3919 83.4156 0.3439 -0.0385 0.346 353.6194 0.1335 -0.1577 0.2067 310.2558

195 0.1038 0.3849 0.3987 74.9035 0.2697 -0.0325 0.2716 353.1312 0.1227 -0.128 0.1773 313.7686

200 0.1257 0.3718 0.3925 71.3167 0.2273 -0.0292 0.2292 352.6688 0.115 -0.1086 0.1581 316.6554

205 0.1315 0.3563 0.3798 69.7485 0.2 -0.0274 0.2019 352.195 0.1091 -0.0942 0.1441 319.2176

210 0.1292 0.3402 0.3639 69.2119 0.1806 -0.0264 0.1826 351.6942 0.1043 -0.0827 0.1331 321.5974

215 0.1339 0.3193 0.3462 67.2522 0.148 -0.0225 0.1497 351.3659 0.0937 -0.0673 0.1154 324.3383

220 0.1235 0.3028 0.327 67.8166 0.1371 -0.0222 0.1389 350.8063 0.0897 -0.0593 0.1075 326.5506

225 0.1121 0.2865 0.3077 68.6248 0.1272 -0.022 0.1291 350.1949 0.0858 -0.0521 0.1004 328.729

230 0.1005 0.2703 0.2884 69.5955 0.1179 -0.0218 0.1199 349.5063 0.0818 -0.0455 0.0936 330.8971

235 0.0891 0.2541 0.2693 70.6696 0.1085 -0.0217 0.1106 348.705 0.0775 -0.0394 0.0869 333.0822

240 0.0783 0.2381 0.2506 71.8016 0.0988 -0.0215 0.1011 347.7406 0.0729 -0.0335 0.0802 335.3235

245 0.0681 0.2221 0.2323 72.9564 0.0887 -0.0212 0.0912 346.5406 0.0678 -0.0278 0.0733 337.6836

250 0.0587 0.2061 0.2143 74.1075 0.0782 -0.0209 0.0809 344.9966 0.0621 -0.0223 0.066 340.2679

255 0.0501 0.1901 0.1966 75.2365 0.0671 -0.0206 0.0702 342.9381 0.0557 -0.0167 0.0582 343.2624

260 0.0423 0.1738 0.1789 76.3331 0.0556 -0.0202 0.0591 340.0749 0.0485 -0.0112 0.0498 347.0183

265 0.0344 0.1595 0.1632 77.8262 0.0458 -0.0208 0.0503 335.5995 0.0423 -0.0066 0.0428 351.1671

270 0.0282 0.1415 0.1443 78.7402 0.0328 -0.0197 0.0383 328.9891 0.0329 -0.0004 0.0329 359.3015

275 0.0216 0.1186 0.1205 79.6643 0.0186 -0.0178 0.0257 316.2407 0.0244 0.009 0.026 20.2182

280 0.016 0.0972 0.0985 80.6783 0.0054 -0.016 0.0169 288.7388 0.0132 0.0158 0.0206 50.1001

285 0.0103 0.073 0.0737 81.9327 -0.0078 -0.0135 0.0156 239.8998 0.0011 0.0231 0.0231 87.3092

290 0.0047 0.0449 0.0451 84.0834 -0.0212 -0.0101 0.0235 205.3962 -0.0119 0.031 0.0332 111.0727

295 -0.0013 0.0115 0.0116 96.4898 -0.0349 -0.0053 0.0353 188.6255 -0.0259 0.0398 0.0475 123.0756

300 -0.0078 -0.0291 0.0301 254.9872 -0.0488 0.0014 0.0488 178.3568 -0.041 0.0498 0.0645 129.4322

305 -0.0152 -0.0793 0.0808 259.1599 -0.063 0.0107 0.0638 170.3926 -0.0572 0.0614 0.0839 132.9702

310 -0.0241 -0.1429 0.145 260.4114 -0.0773 0.0233 0.0808 163.1991 -0.0748 0.075 0.1059 134.9002

315 -0.0358 -0.2254 0.2282 260.9761 -0.0916 0.0406 0.1002 156.0915 -0.0942 0.0916 0.1314 135.7881

320 -0.0529 -0.3406 0.3447 261.1781 -0.1063 0.0654 0.1248 148.4226 -0.116 0.114 0.1626 135.5083

325 -0.0784 -0.4957 0.5018 261.0131 -0.1167 0.0969 0.1516 140.3027 -0.1419 0.1411 0.2001 135.1557

330 -0.1231 -0.7339 0.7441 260.4808 -0.1192 0.1403 0.1841 130.3612 -0.1744 0.1792 0.25 134.2258

335 -0.2542 -1.3201 1.3444 259.0998 -0.0788 0.2187 0.2325 109.8272 -0.236 0.2574 0.3492 132.5098

340 -0.6014 -2.5866 2.6556 256.9118 0.1099 0.317 0.3355 70.8749 -0.312 0.3764 0.4889 129.6529

345 -2.7578 -8.9546 9.3697 252.8827 1.7289 0.3396 1.7619 11.1114 -0.3471 0.5983 0.6917 120.1176

350 -117.5245 -241.7057 268.7632 244.0696 118.1372 -38.1501 124.1444 342.1031 28.2673 -25.2594 37.9088 318.2163

355 -1.6137 -1.3067 2.0764 218.9998 2.0705 -1.2248 2.4056 329.3928 0.8907 -1.043 1.3715 310.4946

360 -0.3608 0.2091 0.417 149.9094 0.4866 -0.3797 0.6172 322.0362 0.2829 -0.3878 0.48 306.1164

Appendix A12


theta2

degree

F32x

/10.^6

N

F32y

/10.^6

N

F32

/10.^6

N

theta32

degree

F43x

/10.^6

N

F43y

/10.^6

N

F43

/10.^6

N

theta43

degree

F53x

/10.^6

N

F53y

/10.^6

N

F53

/10.^6

N

theta53

degree

F65x

/10.^6

N

F65y

/10.^6

N

F65

/10.^6

N

theta65

degree

T/10.^3

N.m

0 0.3269 -0.2094 0.3882 327.352 0.3925 0.2561 0.4686 33.1306 -0.3301 -0.6738 0.7503 243.899 0.3271 -0.1172 0.3474 340.282 63.6387

5 0.1751 -0.2234 0.2838 308.097 0.216 0.1239 0.249 29.8367 -0.2119 -0.4532 0.5003 244.941 0.1986 -0.0833 0.2153 337.257 72.2582

10 0.1284 -0.174 0.2162 306.431 0.147 0.0883 0.1715 30.9928 -0.1518 -0.3326 0.3656 245.476 0.1405 -0.0584 0.1522 337.444 58.8212

15 0.1137 -0.1248 0.1688 312.332 0.1152 0.0782 0.1392 34.1725 -0.1143 -0.2587 0.2828 246.167 0.1128 -0.0387 0.1193 341.059 45.54

20 0.1058 -0.0972 0.1437 317.433 0.1004 0.072 0.1236 35.6566 -0.0942 -0.2189 0.2383 246.724 0.0966 -0.0293 0.1009 343.141 38.7091

25 0.0987 -0.0861 0.131 318.894 0.0939 0.0664 0.115 35.2741 -0.0849 -0.2004 0.2177 247.037 0.0879 -0.0254 0.0915 343.898 36.3542

30 0.0891 -0.0891 0.126 315.025 0.0916 0.0602 0.1096 33.3178 -0.0841 -0.1977 0.2148 246.948 0.0835 -0.0259 0.0874 342.747 36.9482

35 0.076 -0.1029 0.1279 306.453 0.0915 0.0536 0.106 30.3533 -0.09 -0.2066 0.2254 246.457 0.0816 -0.03 0.0869 339.841 38.8377

40 0.0568 -0.1289 0.1409 293.793 0.0928 0.046 0.1035 26.3545 -0.1038 -0.2274 0.25 245.462 0.0786 -0.0397 0.088 333.215 41.0884

45 0.037 -0.1555 0.1598 283.395 0.0947 0.0401 0.1028 22.9446 -0.1191 -0.2508 0.2777 244.597 0.0788 -0.0477 0.0921 328.816 41.3568

50 0.015 -0.1848 0.1854 274.651 0.0971 0.035 0.1032 19.834 -0.1372 -0.2778 0.3098 243.723 0.0794 -0.0564 0.0974 324.594 39.5879

55 -0.0082 -0.2149 0.215 267.802 0.0998 0.0309 0.1045 17.1837 -0.1568 -0.3064 0.3442 242.899 0.0801 -0.0652 0.1033 320.874 35.3926

60 -0.032 -0.2442 0.2463 262.544 0.1026 0.0276 0.1062 15.0397 -0.177 -0.335 0.3789 242.153 0.0809 -0.0734 0.1092 317.784 28.6903

65 -0.0554 -0.2718 0.2774 258.486 0.1054 0.0251 0.1083 13.3757 -0.1967 -0.3623 0.4122 241.493 0.0816 -0.0807 0.1148 315.331 19.6433

70 -0.0778 -0.2967 0.3068 255.3 0.108 0.0232 0.1105 12.1308 -0.2153 -0.3872 0.4431 240.919 0.0824 -0.0869 0.1197 313.459 8.5905

75 -0.0989 -0.3185 0.3335 252.747 0.1103 0.0219 0.1124 11.2354 -0.2322 -0.4091 0.4704 240.428 0.083 -0.0919 0.1238 312.088 -4.0141

80 -0.1155 -0.3284 0.3481 250.632 0.1107 0.0249 0.1134 12.6601 -0.2422 -0.4228 0.4873 240.196 0.0832 -0.0957 0.1268 310.995 -17.2603

85 -0.1329 -0.3426 0.3674 248.802 0.1117 0.0251 0.1145 12.6931 -0.254 -0.4378 0.5061 239.882 0.0838 -0.0987 0.1295 310.334 -31.1984

90 -0.1483 -0.3533 0.3832 247.23 0.1119 0.0256 0.1148 12.9002 -0.2631 -0.4491 0.5205 239.634 0.0844 -0.1007 0.1314 309.963 -45.1296

95 -0.1617 -0.3607 0.3953 245.856 0.1115 0.0262 0.1145 13.2375 -0.2695 -0.4566 0.5302 239.45 0.0848 -0.1017 0.1324 309.829 -58.5725

100 -0.1729 -0.3648 0.4037 244.637 0.1102 0.0268 0.1134 13.6726 -0.273 -0.4603 0.5352 239.326 0.0851 -0.1018 0.1327 309.889 -71.0813

105 -0.182 -0.3656 0.4084 243.54 0.1081 0.0273 0.1115 14.1828 -0.2737 -0.4602 0.5355 239.26 0.0852 -0.1012 0.1323 310.108 -82.2519

110 -0.1887 -0.3631 0.4092 242.539 0.1052 0.0277 0.1088 14.7531 -0.2714 -0.4562 0.5308 239.25 0.0851 -0.0997 0.1311 310.46 -91.7224

115 -0.1949 -0.3579 0.4075 241.43 0.1025 0.0262 0.1058 14.3486 -0.269 -0.4471 0.5218 238.964 0.0828 -0.0954 0.1263 310.942 -99.7375

120 -0.1969 -0.3486 0.4003 240.546 0.0984 0.0259 0.1018 14.7641 -0.2613 -0.4346 0.5071 238.988 0.0815 -0.092 0.1229 311.525 -104.871

125 -0.1959 -0.3355 0.3885 239.719 0.0939 0.0255 0.0973 15.1791 -0.2505 -0.4178 0.4871 239.054 0.0797 -0.0878 0.1186 312.229 -107.347

130 -0.1915 -0.3182 0.3713 238.954 0.0891 0.0249 0.0925 15.6074 -0.2364 -0.3961 0.4613 239.168 0.0772 -0.0825 0.113 313.095 -106.813

135 -0.1826 -0.2954 0.3473 238.276 0.0844 0.0243 0.0878 16.0917 -0.2186 -0.3687 0.4286 239.34 0.074 -0.076 0.1061 314.228 -102.797

140 -0.1674 -0.2654 0.3138 237.763 0.0805 0.0242 0.084 16.7321 -0.1961 -0.3342 0.3875 239.6 0.07 -0.0678 0.0975 315.883 -94.5465

145 -0.1421 -0.2245 0.2657 237.66 0.0786 0.0251 0.0825 17.7335 -0.1671 -0.2898 0.3345 240.027 0.0649 -0.057 0.0864 318.732 -80.6755

150 -0.0986 -0.1645 0.1918 239.065 0.0814 0.0287 0.0863 19.4401 -0.1277 -0.2293 0.2625 240.895 0.059 -0.0414 0.0721 324.899 -58.2798

155 -0.016 -0.0663 0.0682 256.458 0.0957 0.039 0.1033 22.1916 -0.0682 -0.139 0.1548 243.857 0.0527 -0.0161 0.0551 342.987 -20.2629

160 0.174 0.1293 0.2167 36.6172 0.1445 0.0696 0.1604 25.711 0.04 0.0222 0.0458 29.0791 0.0507 0.0349 0.0616 34.5733 55.162

165 1.0327 0.9002 1.3699 41.0774 0.4206 0.2463 0.4874 30.3515 0.418 0.5592 0.6982 53.2231 0.1054 0.2376 0.2599 66.0835 346.01

170 11.6149 8.7006 14.512 36.8364 4.3774 2.5844 5.0833 30.5572 3.8288 5.0073 6.3034 52.5964 1.572 2.4855 2.9409 57.6874 3221.2

175 8.3993 3.9602 9.2861 25.2433 3.8435 2.0642 4.3627 28.2391 1.1215 0.708 1.3263 32.2625 2.2711 1.4599 2.6999 32.7333 1423.4

180 0.7873 -0.1272 0.7975 350.821 0.5509 0.2475 0.6039 24.1915 -0.2417 -0.5719 0.6209 247.086 0.4776 0.0668 0.4823 7.9645 -38.6196

185 0.1542 -0.3557 0.3877 293.432 0.2393 0.0821 0.253 18.9348 -0.2706 -0.5296 0.5948 242.936 0.2734 -0.0308 0.2751 353.576 -111.835

190 -0.0116 -0.3838 0.384 268.276 0.1454 0.0324 0.1489 12.5533 -0.252 -0.4712 0.5343 241.863 0.2013 -0.0516 0.2078 345.636 -114.319

195 -0.0711 -0.3765 0.3832 259.309 0.104 0.01 0.1045 5.4666 -0.23 -0.422 0.4806 241.403 0.1642 -0.0562 0.1736 341.096 -104.979

200 -0.0939 -0.3606 0.3726 255.408 0.0822 -0.0024 0.0823 358.329 -0.21 -0.3809 0.435 241.136 0.1408 -0.056 0.1515 338.294 -93.2559

205 -0.1007 -0.3424 0.3569 253.604 0.0696 -0.0099 0.0703 351.88 -0.1921 -0.3456 0.3954 240.935 0.1239 -0.054 0.1351 336.428 -81.387

210 -0.0998 -0.3236 0.3387 252.863 0.0617 -0.0147 0.0635 346.598 -0.1761 -0.3143 0.3603 240.746 0.1105 -0.0513 0.1218 335.075 -70.0228

215 -0.1061 -0.3002 0.3184 250.536 0.0442 -0.0232 0.0499 332.321 -0.1538 -0.2717 0.3122 240.491 0.0907 -0.048 0.1026 332.13 -56.2364

220 -0.0975 -0.2814 0.2978 250.889 0.041 -0.0247 0.0479 328.937 -0.1405 -0.2458 0.2832 240.245 0.0811 -0.0447 0.0926 331.125 -46.453

225 -0.0882 -0.2629 0.2773 251.462 0.0384 -0.0255 0.0461 326.458 -0.1283 -0.2217 0.2561 239.947 0.0723 -0.0416 0.0834 330.1 -37.5314

230 -0.0787 -0.2447 0.257 252.16 0.0357 -0.0257 0.044 324.289 -0.1167 -0.1988 0.2305 239.577 0.0639 -0.0385 0.0746 328.937 -29.4408

235 -0.0697 -0.2267 0.2372 252.912 0.0326 -0.0256 0.0415 321.824 -0.1058 -0.1768 0.206 239.112 0.0557 -0.0355 0.066 327.504 -22.1447

240 -0.0613 -0.2091 0.2179 253.656 0.0288 -0.0256 0.0385 318.39 -0.0952 -0.1555 0.1823 238.516 0.0476 -0.0325 0.0576 325.618 -15.6059

245 -0.0537 -0.1917 0.1991 254.339 0.0241 -0.0257 0.0353 313.162 -0.0849 -0.1345 0.1591 237.735 0.0394 -0.0297 0.0493 322.998 -9.7917

250 -0.0471 -0.1746 0.1809 254.909 0.0184 -0.0262 0.032 305.114 -0.0748 -0.1137 0.1361 236.674 0.031 -0.0268 0.041 319.15 -4.6776

255 -0.0413 -0.1577 0.163 255.319 0.0117 -0.0272 0.0295 293.244 -0.0646 -0.0928 0.1131 235.154 0.0224 -0.0239 0.0327 313.096 -0.2521

260 -0.0364 -0.1408 0.1454 255.514 0.0038 -0.0286 0.0289 277.589 -0.0544 -0.0717 0.09 232.8 0.0134 -0.0209 0.0249 302.679 3.478

265 -0.0315 -0.1261 0.13 255.995 -0.0031 -0.0301 0.0303 264.068 -0.0458 -0.0536 0.0705 229.49 0.0059 -0.0183 0.0192 287.938 6.2002

270 -0.0282 -0.108 0.1116 255.378 -0.0137 -0.0328 0.0356 247.297 -0.0345 -0.0302 0.0458 221.181 -0.0043 -0.0149 0.0155 253.868 8.5742

275 -0.0246 -0.0852 0.0887 253.903 -0.0264 -0.0349 0.0438 232.944 -0.0209 -0.0029 0.0211 187.783 -0.013 -0.0082 0.0154 212.089 9.7018

280 -0.0218 -0.0642 0.0678 251.206 -0.0386 -0.0375 0.0538 224.127 -0.0088 0.0227 0.0243 111.103 -0.024 -0.004 0.0244 189.441 9.9204

285 -0.0191 -0.0406 0.0449 244.796 -0.0517 -0.0395 0.0651 217.343 0.0041 0.0499 0.05 85.293 -0.0355 0.0007 0.0355 178.803 8.796

290 -0.0162 -0.0134 0.0211 219.563 -0.0656 -0.0404 0.0771 211.582 0.0179 0.0792 0.0812 77.2701 -0.0474 0.0062 0.0478 172.519 6.0116

295 -0.013 0.0188 0.0229 124.639 -0.0805 -0.0395 0.0896 206.138 0.0329 0.1112 0.116 73.5456 -0.06 0.0127 0.0613 168.045 1.1272

300 -0.0092 0.0581 0.0588 98.963 -0.0963 -0.036 0.1028 200.496 0.0494 0.147 0.1551 71.4247 -0.0732 0.0205 0.076 164.39 -6.4668

305 -0.0043 0.1067 0.1068 92.2814 -0.1133 -0.0288 0.1169 194.248 0.0681 0.1877 0.1997 70.0705 -0.0874 0.0299 0.0924 161.093 -17.6247

310 0.0024 0.1685 0.1686 89.1993 -0.1316 -0.0163 0.1326 187.056 0.0897 0.2353 0.2519 69.1429 -0.1028 0.0417 0.111 157.903 -33.5762

315 0.0118 0.249 0.2493 87.2819 -0.1515 0.0036 0.1516 178.645 0.1155 0.2929 0.3148 68.4789 -0.12 0.0568 0.1328 154.664 -56.1837

320 0.0269 0.3621 0.3631 85.7514 -0.1749 0.0357 0.1785 168.456 0.1497 0.3688 0.398 67.9062 -0.1399 0.0782 0.1603 150.795 -89.7339

325 0.0506 0.5147 0.5172 84.3837 -0.1991 0.0834 0.2159 157.265 0.1919 0.4652 0.5032 67.5809 -0.1643 0.1057 0.1954 147.227 -137.221

330 0.0937 0.7504 0.7563 82.883 -0.2267 0.1623 0.2788 144.392 0.2529 0.6064 0.657 67.3621 -0.1963 0.1474 0.2454 143.099 -212.1

335 0.2235 1.3341 1.3527 80.4897 -0.2646 0.3705 0.4552 125.534 0.3892 0.9335 1.0114 67.3705 -0.2614 0.2467 0.3594 136.657 -396.747

340 0.5695 2.5978 2.6595 77.6351 -0.273 0.8639 0.906 107.537 0.6443 1.5622 1.6898 67.5867 -0.3489 0.4503 0.5696 127.765 -802.197

345 2.725 8.963 9.3681 73.0892 0.1692 3.6741 3.678 87.3638 1.6302 4.145 4.4541 68.5311 -0.4425 1.3814 1.4506 107.763 -2849.2

350 117.491 241.711 268.75 64.0765 59.2786 136.871 149.157 66.5827 10.306 44.5414 45.7181 76.9721 27.5341 27.1434 38.6638 44.5907 -78644

355 1.5799 1.3093 2.052 39.6493 1.3827 1.5494 2.0767 48.253 -0.67 -1.1754 1.3529 240.316 0.9486 -0.07 0.9512 355.78 -438.908

360 0.3269 -0.2094 0.3882 327.352 0.3925 0.2561 0.4686 33.1306 -0.3301 -0.6738 0.7503 243.899 0.3271 -0.1172 0.3474 340.282 63.6387

Appendix A13


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 4.664 20.319 20.8474 77.0723 2.1534 -6.0485 6.4204 289.5965 3.0768 -4.3761 5.3495 305.1104

5 3.3141 12.7451 13.1689 75.4244 1.0797 -3.5843 3.7434 286.7647 1.8782 -2.8887 3.4456 303.0307

10 2.6482 9.0587 9.4379 73.7041 0.6144 -2.4035 2.4807 284.3391 1.2736 -2.1189 2.4722 301.0084

15 2.246 6.9481 7.3021 72.0864 0.3757 -1.7089 1.7497 282.399 0.9639 -1.6535 1.9139 300.2404

20 2.0402 5.7731 6.123 70.537 0.2499 -1.2971 1.321 280.907 0.7747 -1.4111 1.6098 298.7655

25 1.9683 5.1496 5.5129 69.0821 0.1806 -1.0419 1.0575 279.8309 0.6678 -1.2909 1.4534 297.3527

30 2.0045 4.8944 5.2889 67.7284 0.1414 -0.8816 0.8929 279.1122 0.6117 -1.2551 1.3962 295.9828

35 2.1286 4.8913 5.3344 66.4819 0.1193 -0.7777 0.7868 278.7185 0.5876 -1.278 1.4066 294.6929

40 2.3464 5.1019 5.6156 65.302 0.1082 -0.717 0.7251 278.5782 0.5585 -1.3717 1.4811 292.1553

45 2.5906 5.3777 5.9692 64.2785 0.1029 -0.6611 0.669 278.8474 0.5674 -1.4557 1.5623 291.2958

50 2.8674 5.7167 6.3955 63.3619 0.1022 -0.6132 0.6217 279.46 0.5847 -1.549 1.6557 290.681

55 3.1604 6.0829 6.8549 62.5453 0.1044 -0.5689 0.5784 280.4013 0.6077 -1.6414 1.7503 290.3142

60 3.4548 6.4489 7.316 61.821 0.1083 -0.5258 0.5368 281.6426 0.6344 -1.7255 1.8384 290.1874

65 3.738 6.7942 7.7546 61.1813 0.1129 -0.4831 0.4962 283.1473 0.6639 -1.7962 1.915 290.2862

70 3.9996 7.1037 8.1522 60.619 0.1171 -0.4407 0.4559 284.8769 0.6954 -1.8509 1.9772 290.593

75 4.2315 7.3669 8.4957 60.1275 0.1202 -0.3984 0.4161 286.7952 0.7283 -1.8885 2.0241 291.089

80 4.3848 7.4068 8.6074 59.3743 0.0932 -0.2555 0.272 290.0406 0.7588 -1.9143 2.0592 291.6223

85 4.5458 7.5474 8.8107 58.9396 0.084 -0.1978 0.2149 293.011 0.7944 -1.9254 2.0828 292.4211

90 4.6675 7.6343 8.9481 58.559 0.0714 -0.1428 0.1596 296.5838 0.8302 -1.9224 2.094 293.3564

95 4.7478 7.6663 9.0174 58.2296 0.0556 -0.0912 0.1068 301.3414 0.8653 -1.9064 2.0936 294.4119

100 4.7854 7.6432 9.0177 57.9495 0.0366 -0.0439 0.0571 309.8074 0.8989 -1.8785 2.0825 295.5717

105 4.7792 7.5649 8.9481 57.7168 0.0148 -0.0013 0.0149 354.9429 0.93 -1.8395 2.0612 296.8212

110 4.7287 7.4313 8.8083 57.5303 -0.0091 0.036 0.0372 104.2276 0.9577 -1.7901 2.0301 298.1463

115 4.6615 7.2485 8.618 57.2551 -0.0176 0.04 0.0437 113.7412 0.9507 -1.6939 1.9424 299.304

120 4.5234 7.0006 8.3348 57.1317 -0.039 0.061 0.0724 122.587 0.9599 -1.6173 1.8807 300.6911

125 4.3381 6.6921 7.9752 57.0471 -0.0595 0.0757 0.0963 128.197 0.9597 -1.5295 1.8057 302.1057

130 4.1027 6.3174 7.5326 56.9992 -0.0782 0.084 0.1148 132.9741 0.9474 -1.4295 1.715 303.5347

135 3.8116 5.866 6.9955 56.9852 -0.0941 0.0862 0.1277 137.5047 0.9197 -1.3151 1.6048 304.9655

140 3.4543 5.3192 6.3424 57.0007 -0.1058 0.0828 0.1344 141.9558 0.8713 -1.1823 1.4687 306.3871

145 3.0099 4.6422 5.5326 57.0417 -0.1108 0.0742 0.1333 146.1959 0.7938 -1.0236 1.2953 307.7933

150 2.4344 3.7659 4.4842 57.1199 -0.1028 0.061 0.1196 149.3076 0.6718 -0.8236 1.0628 309.1999

155 1.6226 2.5378 3.0122 57.4067 -0.0617 0.0441 0.0758 144.4445 0.4727 -0.5483 0.7239 310.7694

160 0.2654 0.5558 0.6159 64.4737 0.0971 0.0238 0.1 13.7574 0.1131 -0.1038 0.1535 317.4673

165 -3.8941 -4.9061 6.2637 231.5596 1.1079 0.0322 1.1083 1.6667 -0.9398 1.1484 1.4839 129.2965

170 -36.7519 -31.2492 48.2412 220.3737 20.2567 0.0378 20.2568 0.1068 -6.0841 8.6423 10.5691 125.1452

175 -4.2442 32.8831 33.1559 97.3544 25.2785 -0.4283 25.2821 359.0294 7.1059 -4.3032 8.3073 328.8016

180 4.3983 15.3249 15.9436 73.9862 4.6739 -0.1759 4.6772 357.8444 3.3474 -2.7274 4.3179 320.828

185 3.8557 11.0357 11.6899 70.7413 2.4991 -0.1492 2.5036 356.5827 2.4997 -2.031 3.2208 320.9054

190 3.2732 9.0145 9.5904 70.0436 1.8128 -0.1515 1.8191 355.2233 2.0969 -1.6795 2.6865 321.3078

195 2.7872 7.7473 8.2334 70.2134 1.504 -0.1611 1.5126 353.8842 1.8474 -1.4472 2.3468 321.9251

200 2.3814 6.8313 7.2345 70.7816 1.3355 -0.1735 1.3467 352.5985 1.6663 -1.2743 2.0977 322.5922

205 2.0361 6.1075 6.438 71.5627 1.2285 -0.1865 1.2426 351.3673 1.5205 -1.1356 1.8978 323.2455

210 1.7379 5.4999 5.7679 72.464 1.1497 -0.1991 1.1669 350.1768 1.3944 -1.0185 1.7268 323.8535

215 1.3833 4.6255 4.8279 73.3499 1.0068 -0.1753 1.0219 350.1225 1.1958 -0.8641 1.4753 324.1491

220 1.1608 4.157 4.316 74.3979 0.949 -0.1832 0.9665 349.0737 1.0893 -0.7746 1.3366 324.5832

225 0.9663 3.7244 3.8477 75.4555 0.8894 -0.1889 0.9093 348.0098 0.9867 -0.693 1.2057 324.9182

230 0.7956 3.3164 3.4105 76.5098 0.8259 -0.192 0.8479 346.9136 0.8858 -0.6171 1.0795 325.1348

235 0.6454 2.9245 2.9949 77.5544 0.7569 -0.1919 0.7808 345.7739 0.7849 -0.5454 0.9557 325.2065

240 0.5131 2.5418 2.5931 78.5884 0.6817 -0.188 0.7072 344.5837 0.6826 -0.4764 0.8324 325.0921

245 0.3962 2.1625 2.1985 79.6173 0.5999 -0.1795 0.6262 343.337 0.5779 -0.4089 0.708 324.7214

250 0.2931 1.7813 1.8053 80.6569 0.5108 -0.1657 0.537 342.0267 0.4699 -0.3419 0.5811 323.9613

255 0.2021 1.3934 1.408 81.7466 0.414 -0.1455 0.4388 340.6398 0.3576 -0.2742 0.4507 322.5169

260 0.1221 0.9941 1.0016 82.9995 0.3089 -0.1177 0.3305 339.1463 0.2405 -0.205 0.316 319.5643

265 0.0637 0.6572 0.6603 84.4667 0.2146 -0.093 0.2338 336.5647 0.1403 -0.1457 0.2022 313.9265

270 -0.0023 0.1973 0.1973 90.6797 0.0862 -0.0415 0.0957 334.294 0.0057 -0.0663 0.0665 274.8777

275 -0.0661 -0.3223 0.329 258.4054 -0.0639 0.0285 0.07 156.0026 -0.116 0.0478 0.1254 157.6176

280 -0.116 -0.8368 0.8448 262.1105 -0.2124 0.107 0.2378 153.2728 -0.2626 0.1388 0.297 152.1417

285 -0.1604 -1.3902 1.3994 263.4166 -0.3723 0.2031 0.4241 151.3849 -0.416 0.2383 0.4794 150.1943

290 -0.2018 -1.9934 2.0036 264.2183 -0.5446 0.3209 0.6321 149.4929 -0.5773 0.3488 0.6745 148.8617

295 -0.2432 -2.661 2.6721 264.7776 -0.7309 0.4656 0.8666 147.4978 -0.7479 0.4733 0.8851 147.6717

300 -0.2888 -3.4123 3.4245 265.1618 -0.9327 0.6443 1.1336 145.363 -0.9302 0.6162 1.1158 146.4761

305 -0.3448 -4.2745 4.2884 265.3881 -1.1524 0.8662 1.4417 143.0677 -1.1276 0.7834 1.373 145.2113

310 -0.4202 -5.2872 5.3039 265.4554 -1.3933 1.1445 1.8031 140.5985 -1.3457 0.9833 1.6667 143.8441

315 -0.5291 -6.5112 6.5326 265.3545 -1.6608 1.4982 2.2367 137.9476 -1.5937 1.2293 2.0127 142.3554

320 -0.7041 -8.1214 8.1519 265.0451 -1.987 1.9799 2.805 135.1031 -1.8839 1.5666 2.4501 140.2541

325 -0.9623 -10.1322 10.1778 264.5747 -2.3414 2.5919 3.4929 132.0935 -2.2536 1.9829 3.0018 138.6553

330 -1.3907 -12.9926 13.0668 263.8905 -2.7935 3.4602 4.4471 128.914 -2.7616 2.5866 3.7837 136.8742

335 -2.4735 -19.2473 19.4056 262.677 -3.6418 5.3196 6.4468 124.3958 -3.8911 3.9212 5.5242 134.779

340 -4.4958 -29.8957 30.2319 261.4478 -5.0119 8.3029 9.6982 121.1164 -5.7875 6.2977 8.5531 132.5826

345 -11.6791 -63.7711 64.8317 259.6218 -8.8348 16.9534 19.1173 117.525 -11.985 14.3189 18.6727 129.9294

350 23.6247 487.7587 488.3305 87.227 122.5997 -227.3696 258.3169 298.3339 62.8228 -51.3252 81.1232 320.7517

355 9.2713 49.6292 50.4878 79.4185 6.8142 -15.9104 17.3082 293.1847 7.7262 -9.9067 12.5634 307.9507

360 4.664 20.319 20.8474 77.0723 2.1534 -6.0485 6.4204 289.5965 3.0768 -4.3761 5.3495 305.1104

Appendix A13


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 -4.664 -20.319 20.847 257.072 2.1534 -6.0485 6.4204 289.597 -6.8182 -14.2711 15.8162 244.463 3.0768 -4.3761 5.3495 305.11 618.306

5 -3.3141 -12.745 13.169 255.424 1.0797 -3.5843 3.7434 286.765 -4.3944 -9.1613 10.1607 244.374 1.8782 -2.8887 3.4456 303.031 377.567

10 -2.6482 -9.0587 9.4379 253.704 0.6144 -2.4035 2.4807 284.339 -3.2631 -6.6556 7.4125 243.882 1.2736 -2.1189 2.4722 301.008 257.475

15 -2.246 -6.9481 7.3021 252.086 0.3757 -1.7089 1.7497 282.399 -2.6221 -5.2395 5.859 243.414 0.9639 -1.6535 1.9139 300.24 186.536

20 -2.0402 -5.7731 6.123 250.537 0.2499 -1.2971 1.321 280.907 -2.2905 -4.4763 5.0283 242.902 0.7747 -1.4111 1.6098 298.766 143.847

25 -1.9683 -5.1496 5.5129 249.082 0.1806 -1.0419 1.0575 279.831 -2.1492 -4.1079 4.6362 242.382 0.6678 -1.2909 1.4534 297.353 116.707

30 -2.0045 -4.8944 5.2889 247.728 0.1414 -0.8816 0.8929 279.112 -2.1462 -4.013 4.5509 241.861 0.6117 -1.2551 1.3962 295.983 98.4838

35 -2.1286 -4.8913 5.3344 246.482 0.1193 -0.7777 0.7868 278.719 -2.2482 -4.1138 4.6881 241.343 0.5876 -1.278 1.4066 294.693 84.771

40 -2.3464 -5.1019 5.6156 245.302 0.1082 -0.717 0.7251 278.578 -2.4549 -4.3851 5.0255 240.759 0.5585 -1.3717 1.4811 292.155 73.0337

45 -2.5906 -5.3777 5.9692 244.279 0.1029 -0.6611 0.669 278.847 -2.6938 -4.7169 5.4319 240.27 0.5674 -1.4557 1.5623 291.296 59.9709

50 -2.8674 -5.7167 6.3955 243.362 0.1022 -0.6132 0.6217 279.46 -2.9699 -5.1036 5.9049 239.804 0.5847 -1.549 1.6557 290.681 44.9759

55 -3.1604 -6.0829 6.8549 242.545 0.1044 -0.5689 0.5784 280.401 -3.2651 -5.5142 6.4084 239.369 0.6077 -1.6414 1.7503 290.314 27.3907

60 -3.4548 -6.4489 7.316 241.821 0.1083 -0.5258 0.5368 281.643 -3.5634 -5.9233 6.9125 238.969 0.6344 -1.7255 1.8384 290.187 7.0745

65 -3.738 -6.7942 7.7546 241.181 0.1129 -0.4831 0.4962 283.147 -3.8511 -6.3112 7.3933 238.609 0.6639 -1.7962 1.915 290.286 -15.7156

70 -3.9996 -7.1037 8.1522 240.619 0.1171 -0.4407 0.4559 284.877 -4.1168 -6.6631 7.8324 238.29 0.6954 -1.8509 1.9772 290.593 -40.4355

75 -4.2315 -7.3669 8.4957 240.128 0.1202 -0.3984 0.4161 286.795 -4.3519 -6.9687 8.2159 238.016 0.7283 -1.8885 2.0241 291.089 -66.3549

80 -4.3848 -7.4068 8.6074 239.374 0.0932 -0.2555 0.272 290.041 -4.4782 -7.1513 8.4378 237.945 0.7588 -1.9143 2.0592 291.622 -92.2654

85 -4.5458 -7.5474 8.8107 238.94 0.084 -0.1978 0.2149 293.011 -4.6299 -7.3497 8.6865 237.791 0.7944 -1.9254 2.0828 292.421 -117.785

90 -4.6675 -7.6343 8.9481 238.559 0.0714 -0.1428 0.1596 296.584 -4.7391 -7.4916 8.8647 237.683 0.8302 -1.9224 2.094 293.356 -142.032

95 -4.7478 -7.6663 9.0174 238.23 0.0556 -0.0912 0.1068 301.341 -4.8035 -7.5752 8.9698 237.621 0.8653 -1.9064 2.0936 294.412 -164.259

100 -4.7854 -7.6432 9.0177 237.95 0.0366 -0.0439 0.0571 309.807 -4.822 -7.5994 9.0001 237.604 0.8989 -1.8785 2.0825 295.572 -183.794

105 -4.7792 -7.5649 8.9481 237.717 0.0148 -0.0013 0.0149 354.943 -4.7941 -7.5636 8.955 237.632 0.93 -1.8395 2.0612 296.821 -200.056

110 -4.7287 -7.4313 8.8083 237.53 -0.0091 0.036 0.0372 104.228 -4.7197 -7.4674 8.8338 237.706 0.9577 -1.7901 2.0301 298.146 -212.56

115 -4.6615 -7.2485 8.618 237.255 -0.0176 0.04 0.0437 113.741 -4.6439 -7.2885 8.6422 237.497 0.9507 -1.6939 1.9424 299.304 -221.776

120 -4.5234 -7.0006 8.3348 237.132 -0.039 0.061 0.0724 122.587 -4.4844 -7.0616 8.3652 237.583 0.9599 -1.6173 1.8807 300.691 -225.72

125 -4.3381 -6.6921 7.9752 237.047 -0.0595 0.0757 0.0963 128.197 -4.2786 -6.7678 8.0068 237.699 0.9597 -1.5295 1.8057 302.106 -224.939

130 -4.1027 -6.3174 7.5326 236.999 -0.0782 0.084 0.1148 132.974 -4.0244 -6.4013 7.5612 237.843 0.9474 -1.4295 1.715 303.535 -219.204

135 -3.8116 -5.866 6.9955 236.985 -0.0941 0.0862 0.1277 137.505 -3.7174 -5.9522 7.0176 238.014 0.9197 -1.3151 1.6048 304.966 -208.234

140 -3.4543 -5.3192 6.3424 237.001 -0.1058 0.0828 0.1344 141.956 -3.3484 -5.402 6.3555 238.208 0.8713 -1.1823 1.4687 306.387 -191.56

145 -3.0099 -4.6422 5.5326 237.042 -0.1108 0.0742 0.1333 146.196 -2.899 -4.7164 5.5361 238.422 0.7938 -1.0236 1.2953 307.793 -168.251

150 -2.4344 -3.7659 4.4842 237.12 -0.1028 0.061 0.1196 149.308 -2.3315 -3.8269 4.4812 238.649 0.6718 -0.8236 1.0628 309.2 -136.283

155 -1.6226 -2.5378 3.0122 237.407 -0.0617 0.0441 0.0758 144.445 -1.5609 -2.5819 3.017 238.845 0.4727 -0.5483 0.7239 310.769 -90.8564

160 -0.2654 -0.5558 0.6159 244.474 0.0971 0.0238 0.1 13.7574 -0.3629 -0.5798 0.684 237.959 0.1131 -0.1038 0.1535 317.467 -18.654

165 3.8941 4.9061 6.2637 51.5596 1.1079 0.0322 1.1083 1.6667 2.7831 4.8712 5.6102 60.2594 -0.9398 1.1484 1.4839 129.297 174.874

170 36.7519 31.2492 48.241 40.3737 20.2567 0.0378 20.2568 0.1068 16.4422 31.1685 35.2395 62.1873 -6.0841 8.6423 10.5691 125.145 1130.7

175 4.2442 -32.883 33.156 277.354 25.2785 -0.4283 25.2821 359.029 -21.0947 -32.5038 38.7489 237.017 7.1059 -4.3032 8.3073 328.802 -985.569

180 -4.3983 -15.325 15.944 253.986 4.6739 -0.1759 4.6772 357.844 -9.0823 -15.1571 17.6699 239.07 3.3474 -2.7274 4.3179 320.828 -466.336

185 -3.8557 -11.036 11.69 250.741 2.4991 -0.1492 2.5036 356.583 -6.3597 -10.8904 12.6114 239.716 2.4997 -2.031 3.2208 320.905 -324.313

190 -3.2732 -9.0145 9.5904 250.044 1.8128 -0.1515 1.8191 355.223 -5.0892 -8.8656 10.2224 240.142 2.0969 -1.6795 2.6865 321.308 -252.848

195 -2.7872 -7.7473 8.2334 250.213 1.504 -0.1611 1.5126 353.884 -4.2934 -7.588 8.7185 240.498 1.8474 -1.4472 2.3468 321.925 -205.767

200 -2.3814 -6.8313 7.2345 250.782 1.3355 -0.1735 1.3467 352.599 -3.7186 -6.6593 7.6272 240.82 1.6663 -1.2743 2.0977 322.592 -170.555

205 -2.0361 -6.1075 6.438 251.563 1.2285 -0.1865 1.2426 351.367 -3.2661 -5.9222 6.7631 241.123 1.5205 -1.1356 1.8978 323.246 -142.254

210 -1.7379 -5.4999 5.7679 252.464 1.1497 -0.1991 1.1669 350.177 -2.8888 -5.3018 6.0377 241.415 1.3944 -1.0185 1.7268 323.854 -118.497

215 -1.3833 -4.6255 4.8279 253.35 1.0068 -0.1753 1.0219 350.123 -2.391 -4.4509 5.0525 241.756 1.1958 -0.8641 1.4753 324.149 -91.1544

220 -1.1608 -4.157 4.316 254.398 0.949 -0.1832 0.9665 349.074 -2.1105 -3.9744 4.5 242.03 1.0893 -0.7746 1.3366 324.583 -74.1969

225 -0.9663 -3.7244 3.8477 255.456 0.8894 -0.1889 0.9093 348.01 -1.8563 -3.536 3.9936 242.301 0.9867 -0.693 1.2057 324.918 -59.3465

230 -0.7956 -3.3164 3.4105 256.51 0.8259 -0.192 0.8479 346.914 -1.6219 -3.1248 3.5207 242.568 0.8858 -0.6171 1.0795 325.135 -46.3227

235 -0.6454 -2.9245 2.9949 257.554 0.7569 -0.1919 0.7808 345.774 -1.4027 -2.733 3.0719 242.83 0.7849 -0.5454 0.9557 325.207 -34.9556

240 -0.5131 -2.5418 2.5931 258.588 0.6817 -0.188 0.7072 344.584 -1.1951 -2.3541 2.6401 243.084 0.6826 -0.4764 0.8324 325.092 -25.1534

245 -0.3962 -2.1625 2.1985 259.617 0.5999 -0.1795 0.6262 343.337 -0.9963 -1.9832 2.2194 243.325 0.5779 -0.4089 0.708 324.721 -16.8831

250 -0.2931 -1.7813 1.8053 260.657 0.5108 -0.1657 0.537 342.027 -0.804 -1.6158 1.8047 243.545 0.4699 -0.3419 0.5811 323.961 -10.1588

255 -0.2021 -1.3934 1.408 261.747 0.414 -0.1455 0.4388 340.64 -0.6162 -1.2481 1.3919 243.724 0.3576 -0.2742 0.4507 322.517 -5.0334

260 -0.1221 -0.9941 1.0016 263 0.3089 -0.1177 0.3305 339.146 -0.431 -0.8765 0.9767 243.815 0.2405 -0.205 0.316 319.564 -1.5948

265 -0.0637 -0.6572 0.6603 264.467 0.2146 -0.093 0.2338 336.565 -0.2783 -0.5642 0.6291 243.748 0.1403 -0.1457 0.2022 313.927 0.187

270 0.0023 -0.1973 0.1973 270.68 0.0862 -0.0415 0.0957 334.294 -0.0839 -0.1558 0.177 241.706 0.0057 -0.0663 0.0665 274.878 -0.0712

275 0.0661 0.3223 0.329 78.4054 -0.0639 0.0285 0.07 156.003 0.1301 0.2938 0.3213 66.1209 -0.116 0.0478 0.1254 157.618 -2.8592

280 0.116 0.8368 0.8448 82.1105 -0.2124 0.107 0.2378 153.273 0.3284 0.7298 0.8003 65.7715 -0.2626 0.1388 0.297 152.142 -7.8964

285 0.1604 1.3902 1.3994 83.4166 -0.3723 0.2031 0.4241 151.385 0.5328 1.1871 1.3012 65.829 -0.416 0.2383 0.4794 150.194 -15.6645

290 0.2018 1.9934 2.0036 84.2183 -0.5446 0.3209 0.6321 149.493 0.7466 1.6726 1.8317 65.9466 -0.5773 0.3488 0.6745 148.862 -26.5187

295 0.2432 2.661 2.6721 84.7776 -0.7309 0.4656 0.8666 147.498 0.9742 2.1954 2.4019 66.0716 -0.7479 0.4733 0.8851 147.672 -40.9288

300 0.2888 3.4123 3.4245 85.1618 -0.9327 0.6443 1.1336 145.363 1.2216 2.7681 3.0257 66.1867 -0.9302 0.6162 1.1158 146.476 -59.5294

305 0.3448 4.2745 4.2884 85.3881 -1.1524 0.8662 1.4417 143.068 1.4973 3.4084 3.7228 66.2834 -1.1276 0.7834 1.373 145.211 -83.2016

310 0.4202 5.2872 5.3039 85.4554 -1.3933 1.1445 1.8031 140.599 1.8137 4.1428 4.5224 66.3561 -1.3457 0.9833 1.6667 143.844 -113.214

315 0.5291 6.5112 6.5326 85.3545 -1.6608 1.4982 2.2367 137.948 2.1901 5.0131 5.4707 66.4006 -1.5937 1.2293 2.0127 142.355 -151.487

320 0.7041 8.1214 8.1519 85.0451 -1.987 1.9799 2.805 135.103 2.6913 6.1417 6.7055 66.3368 -1.8839 1.5666 2.4501 140.254 -203.088

325 0.9623 10.1322 10.178 84.5747 -2.3414 2.5919 3.4929 132.094 3.304 7.5405 8.2325 66.3386 -2.2536 1.9829 3.0018 138.655 -269.359

330 1.3907 12.9926 13.067 83.8905 -2.7935 3.4602 4.4471 128.914 4.1844 9.5326 10.4106 66.3004 -2.7616 2.5866 3.7837 136.874 -363.556

335 2.4735 19.2473 19.406 82.677 -3.6418 5.3196 6.4468 124.396 6.1157 13.928 15.2115 66.2941 -3.8911 3.9212 5.5242 134.779 -562.629

340 4.4958 29.8957 30.232 81.4478 -5.0119 8.3029 9.6982 121.116 9.508 21.5932 23.5938 66.2348 -5.7875 6.2977 8.5531 132.583 -901.654

345 11.6791 63.7711 64.832 79.6218 -8.8348 16.9534 19.1173 117.525 20.5138 46.8176 51.1146 66.3387 -11.985 14.3189 18.6727 129.929 -1966.4

350 -23.625 -487.76 488.33 267.227 122.6 -227.37 258.317 298.334 -146.31 -260.458 298.739 240.675 62.8228 -51.325 81.1232 320.752 14742

355 -9.2713 -49.629 50.488 259.419 6.8142 -15.91 17.3082 293.185 -16.0877 -33.7207 37.3618 244.495 7.7262 -9.9067 12.5634 307.951 1529.1

360 -4.664 -20.319 20.847 257.072 2.1534 -6.0485 6.4204 289.597 -6.8182 -14.2711 15.8162 244.463 3.0768 -4.3761 5.3495 305.11 618.306

Appendix A14


theta2

degree

F12x

/10.^6

N

F12y

/10.^6

N

F12

/10.^6

N

theta12

degree

F14x

/10.^6

N

F14y

/10.^6

N

F14

/10.^6

N

theta14

degree

F16x

/10.^6

N

F16y

/10.^6

N

F16

/10.^6

N

theta16

degree

0 0.4858 -0.6376 0.8016 307.3023 -1.0613 -0.5579 1.199 207.731 0.9938 -0.5482 1.1349 331.1179

5 0.2642 -0.3902 0.4712 304.1086 -0.6454 -0.1523 0.6631 193.28 0.4871 -0.2659 0.5549 331.3729

10 0.164 -0.2745 0.3198 300.8556 -0.5038 -0.0846 0.5109 189.5321 0.3001 -0.1415 0.3318 334.7584

15 0.113 -0.208 0.2367 298.5267 -0.4468 -0.092 0.4562 191.6297 0.2153 -0.0752 0.2281 340.743

20 0.0827 -0.1719 0.1908 295.6956 -0.4162 -0.1014 0.4284 193.6928 0.174 -0.0429 0.1792 346.1456

25 0.0651 -0.1525 0.1659 293.1186 -0.3938 -0.1011 0.4065 194.3938 0.1532 -0.0305 0.1562 348.7339

30 0.0551 -0.1443 0.1544 290.9122 -0.3708 -0.0873 0.3809 193.2523 0.143 -0.0307 0.1463 347.8748

35 0.0498 -0.1437 0.1521 289.1365 -0.3436 -0.0613 0.3491 190.1155 0.1386 -0.0385 0.1439 344.4814

40 0.045 -0.1514 0.1579 286.5501 -0.3089 -0.0215 0.3097 183.9772 0.1377 -0.0513 0.147 339.5519

45 0.0445 -0.159 0.1651 285.6212 -0.2718 0.0202 0.2726 175.7455 0.139 -0.0645 0.1533 335.1192

50 0.0451 -0.1681 0.1741 285.0065 -0.231 0.0653 0.24 164.2186 0.142 -0.0775 0.1618 331.3906

55 0.0464 -0.1775 0.1835 284.6459 -0.1876 0.1112 0.2181 149.35 0.1463 -0.0893 0.1714 328.5973

60 0.0481 -0.1862 0.1923 284.4967 -0.143 0.156 0.2116 132.5211 0.1516 -0.0995 0.1813 326.7167

65 0.0502 -0.1936 0.2 284.529 -0.0983 0.1982 0.2212 116.3737 0.1575 -0.1078 0.1908 325.6192

70 0.0524 -0.1993 0.2061 284.7213 -0.0542 0.2368 0.2429 102.903 0.1637 -0.114 0.1994 325.1532

75 0.0547 -0.2032 0.2104 285.0565 -0.0117 0.2712 0.2714 92.4686 0.1698 -0.1181 0.2069 325.1805

80 0.0567 -0.2049 0.2126 285.4635 0.0247 0.2904 0.2915 85.1365 0.1722 -0.1146 0.2068 326.3406

85 0.0592 -0.2058 0.2141 286.0527 0.0628 0.3147 0.3209 78.7139 0.1768 -0.1139 0.2103 327.2021

90 0.0617 -0.205 0.2141 286.7533 0.0985 0.3346 0.3488 73.5987 0.1804 -0.1115 0.2121 328.2938

95 0.0642 -0.2028 0.2127 287.5566 0.1316 0.3503 0.3742 69.4083 0.1829 -0.1075 0.2122 329.5599

100 0.0665 -0.1993 0.2101 288.4547 0.162 0.3617 0.3963 65.8782 0.184 -0.1021 0.2104 330.9593

105 0.0687 -0.1945 0.2063 289.4406 0.1895 0.3691 0.4149 62.8263 0.1834 -0.0956 0.2068 332.4633

110 0.0706 -0.1887 0.2014 290.5066 0.2139 0.3724 0.4295 60.1251 0.1809 -0.088 0.2012 334.0539

115 0.0696 -0.1786 0.1917 291.3039 0.2377 0.3726 0.4419 57.4583 0.1779 -0.0819 0.1958 335.2682

120 0.0701 -0.1701 0.1839 292.4085 0.2554 0.3672 0.4473 55.1834 0.1717 -0.0732 0.1867 336.9111

125 0.0699 -0.1605 0.175 293.5256 0.2686 0.3569 0.4467 53.0366 0.1634 -0.0639 0.1755 338.6311

130 0.0686 -0.1498 0.1648 294.6089 0.2762 0.3406 0.4385 50.9632 0.153 -0.0543 0.1623 340.4698

135 0.0661 -0.1381 0.1531 295.5693 0.2762 0.3165 0.4201 48.8973 0.1405 -0.0442 0.1473 342.5192

140 0.0616 -0.1251 0.1395 296.2172 0.2648 0.2813 0.3863 46.7282 0.1264 -0.0339 0.1308 344.9801

145 0.0543 -0.1108 0.1233 296.0932 0.2346 0.228 0.3272 44.1839 0.1116 -0.0231 0.114 348.2931

150 0.042 -0.095 0.1039 293.8722 0.1693 0.1424 0.2212 40.0753 0.0994 -0.0116 0.1001 353.3459

155 0.0205 -0.0783 0.0809 284.692 0.026 -0.0116 0.0285 335.9611 0.0997 0.0015 0.0997 0.8677

160 -0.0229 -0.0653 0.0692 250.7095 -0.3365 -0.347 0.4834 225.8831 0.1531 0.0181 0.1542 6.7435

165 -0.1706 -0.1183 0.2076 214.7295 -2.1007 -1.8025 2.768 220.6314 0.6579 0.0556 0.6602 4.8287

170 -1.3782 -1.958 2.3944 234.8584 -25.0311 -17.9984 30.8301 215.7177 10.0966 0.0045 10.0966 0.0253

175 0.0082 -3.043 3.043 270.154 -19.5585 -10.4914 22.1947 208.2095 11.918 -0.6119 11.9337 357.0611

180 0.2338 -0.649 0.6898 289.8144 -2.075 -0.4644 2.1264 192.616 2.1045 -0.1648 2.111 355.5226

185 0.2091 -0.3659 0.4214 299.7492 -0.5405 0.2641 0.6015 153.9591 1.0642 -0.0983 1.0687 354.7245

190 0.192 -0.2642 0.3266 306.0113 -0.1118 0.4324 0.4466 104.498 0.7226 -0.073 0.7263 354.2329

195 0.1808 -0.2107 0.2776 310.6359 0.0584 0.4846 0.4881 83.1283 0.56 -0.0603 0.5633 353.8572

200 0.1731 -0.1764 0.2472 314.4691 0.136 0.5002 0.5184 74.7861 0.4665 -0.0532 0.4695 353.4995

205 0.1676 -0.1515 0.2259 317.882 0.1718 0.5011 0.5297 71.0807 0.4058 -0.049 0.4087 353.1158

210 0.1633 -0.132 0.2099 321.0527 0.1856 0.4949 0.5285 69.4401 0.3625 -0.0465 0.3655 352.6882

215 0.1499 -0.1055 0.1833 324.8577 0.2184 0.4912 0.5375 66.0259 0.2927 -0.0395 0.2953 352.3075

220 0.1463 -0.0922 0.1729 327.7932 0.2087 0.4774 0.521 66.3927 0.2688 -0.0389 0.2716 351.7653

225 0.1428 -0.0803 0.1638 330.6573 0.195 0.4622 0.5017 67.1314 0.2479 -0.0386 0.2509 351.1562

230 0.139 -0.0694 0.1554 333.4728 0.1792 0.4461 0.4807 68.116 0.2285 -0.0384 0.2317 350.4544

235 0.1347 -0.0592 0.1472 336.2661 0.1626 0.4293 0.459 69.2606 0.2096 -0.0384 0.2131 349.6203

240 0.1296 -0.0496 0.1388 339.0748 0.146 0.4123 0.4373 70.5034 0.1906 -0.0384 0.1944 348.5942

245 0.1235 -0.0402 0.1299 341.9583 0.1299 0.3952 0.416 71.7992 0.1711 -0.0386 0.1754 347.2887

250 0.1162 -0.0311 0.1203 345.0115 0.1148 0.3783 0.3954 73.116 0.1511 -0.0389 0.156 345.5731

255 0.1076 -0.0221 0.1098 348.3895 0.1008 0.3617 0.3755 74.4328 0.1305 -0.0393 0.1363 343.2471

260 0.0974 -0.0131 0.0982 352.3553 0.0877 0.3451 0.3561 75.7394 0.1094 -0.0399 0.1165 339.991

265 0.0885 -0.0057 0.0887 356.3255 0.0733 0.3298 0.3379 77.4656 0.0918 -0.0426 0.1012 335.1098

270 0.0741 0.0042 0.0742 3.2502 0.0629 0.3124 0.3187 78.6169 0.0688 -0.043 0.0812 328.0115

275 0.0598 0.0174 0.0623 16.1967 0.052 0.2896 0.2942 79.8199 0.045 -0.0427 0.0621 316.4985

280 0.0419 0.028 0.0504 33.7705 0.0418 0.2674 0.2707 81.1236 0.0228 -0.0428 0.0485 298.0609

285 0.0224 0.0394 0.0453 60.4048 0.0313 0.2409 0.243 82.5967 0.001 -0.0423 0.0423 271.3559

290 0.0011 0.0516 0.0516 88.7779 0.0204 0.2082 0.2092 84.4019 -0.0205 -0.0408 0.0456 243.3023

295 -0.0219 0.0652 0.0687 108.5531 0.0088 0.1668 0.1671 86.9728 -0.0417 -0.0375 0.0561 221.9429

300 -0.0466 0.0804 0.0929 120.1043 -0.0038 0.1136 0.1136 91.9174 -0.0628 -0.0318 0.0704 206.8294

305 -0.0732 0.0979 0.1223 126.799 -0.018 0.0441 0.0477 112.2322 -0.0836 -0.0225 0.0865 195.0416

310 -0.102 0.1185 0.1564 130.7188 -0.0349 -0.0477 0.0591 233.8546 -0.1037 -0.0083 0.104 184.5837

315 -0.1334 0.1434 0.1959 132.9229 -0.0562 -0.1713 0.1802 251.8479 -0.1222 0.0122 0.1228 174.2821

320 -0.1682 0.1767 0.2439 133.5779 -0.0865 -0.3492 0.3597 256.0902 -0.1388 0.0431 0.1453 162.7403

325 -0.2081 0.2169 0.3005 133.8177 -0.1319 -0.5963 0.6107 257.5275 -0.144 0.0824 0.1659 150.2195

330 -0.2562 0.2722 0.3738 133.2573 -0.2124 -0.9875 1.0101 257.8604 -0.1266 0.1352 0.1852 133.1009

335 -0.3392 0.382 0.5109 131.6095 -0.4577 -1.9896 2.0415 257.0454 0.0085 0.2144 0.2146 87.7241

340 -0.4174 0.533 0.677 128.0648 -1.1491 -4.2989 4.4498 255.0341 0.5068 0.2775 0.5778 28.6975

345 -0.1966 0.654 0.6829 106.7325 -5.7168 -16.9006 17.8414 251.3113 4.3744 -0.1517 4.377 358.0134

350 60.1253 -52.3238 79.7046 318.9687 -269.922 -567.7575 628.6543 244.5728 261.6401 -76.3649 272.5567 343.7291

355 1.6189 -1.8078 2.4268 311.8443 -4.1597 -5.4404 6.8485 232.5988 4.3466 -1.9714 4.7728 335.6028

360 0.4858 -0.6376 0.8016 307.3023 -1.0613 -0.5579 1.199 207.731 0.9938 -0.5482 1.1349 331.1179

Appendix A14


theta2

degree

F32x

/10.^6

N

F32y

/10.^6

N

F32

/10.^6

N

theta32

degree

F43x

/10.^6

N

F43y

/10.^6

N

F43

/10.^6

N

theta43

degree

F53x

/10.^6

N

F53y

/10.^6

N

F53

/10.^6

N

theta53

degree

F65x

/10.^6

N

F65y

/10.^6

N

F65

/10.^6

N

theta65

degree

T/10.^3

N.m

0 0.985 0.5579 1.1321 29.5277 0.7846 0.879 1.1782 48.2453 -0.3966 -0.7862 0.8806 243.234 0.5852 -0.0285 0.5859 357.213 -169.782

5 0.5694 0.1457 0.5877 14.351 0.4365 0.4602 0.6343 46.515 -0.2528 -0.5507 0.6059 245.346 0.3562 -0.0315 0.3576 354.941 -29.0587

10 0.4287 0.0714 0.4346 9.45 0.3029 0.3218 0.442 46.7332 -0.1743 -0.4069 0.4426 246.813 0.2559 -0.0162 0.2564 356.379 1.2695

15 0.3731 0.0722 0.38 10.9535 0.2428 0.2635 0.3583 47.3456 -0.1237 -0.3148 0.3382 248.55 0.2074 0.0012 0.2074 0.3358 8.1604

20 0.3446 0.0753 0.3527 12.3313 0.2155 0.2293 0.3147 46.7788 -0.0951 -0.2641 0.2807 250.194 0.1805 0.0098 0.1808 3.0927 14.3218

25 0.3246 0.0688 0.3319 11.969 0.204 0.204 0.2885 44.9887 -0.0814 -0.2413 0.2547 251.356 0.1663 0.0122 0.1667 4.1792 22.7693

30 0.3047 0.0492 0.3086 9.1684 0.2007 0.182 0.2709 42.2023 -0.0798 -0.2401 0.253 251.623 0.1592 0.0088 0.1595 3.1675 33.4004

35 0.2811 0.0176 0.2817 3.5725 0.2015 0.1618 0.2584 38.7697 -0.088 -0.2555 0.2703 250.99 0.1561 0.0006 0.1561 0.2298 44.6956

40 0.2505 -0.0276 0.252 353.722 0.2047 0.1423 0.2493 34.8157 -0.1069 -0.2866 0.3058 249.546 0.1526 -0.0144 0.1533 354.603 55.4156

45 0.2179 -0.0742 0.2302 341.203 0.2091 0.1261 0.2441 31.0899 -0.1294 -0.323 0.348 248.165 0.1526 -0.0286 0.1553 349.384 62.8385

50 0.1819 -0.1237 0.22 325.786 0.2143 0.112 0.2418 27.5977 -0.1564 -0.3648 0.3969 246.8 0.153 -0.0439 0.1592 343.975 66.6116

55 0.1439 -0.1737 0.2255 309.641 0.2201 0.1002 0.2418 24.4821 -0.1859 -0.409 0.4493 245.556 0.1534 -0.0594 0.1645 338.846 66.1797

60 0.1049 -0.222 0.2456 295.287 0.226 0.0904 0.2434 21.8065 -0.2165 -0.4532 0.5023 244.464 0.1537 -0.074 0.1706 334.287 61.427

65 0.066 -0.2673 0.2754 283.875 0.2318 0.0824 0.246 19.5741 -0.2468 -0.4955 0.5535 243.525 0.1537 -0.0873 0.1768 330.417 52.5895

70 0.0282 -0.3085 0.3098 275.216 0.2373 0.076 0.2491 17.7517 -0.2755 -0.5343 0.6012 242.727 0.1536 -0.0988 0.1827 327.242 40.1589

75 -0.0081 -0.3449 0.345 268.663 0.2421 0.0707 0.2522 16.2895 -0.3017 -0.5687 0.6438 242.053 0.1533 -0.1085 0.1878 324.704 24.7953

80 -0.038 -0.3655 0.3675 264.072 0.2441 0.0701 0.254 16.021 -0.3182 -0.5906 0.6709 241.69 0.152 -0.1161 0.1913 322.633 7.9402

85 -0.0694 -0.3907 0.3968 259.92 0.2466 0.0677 0.2557 15.358 -0.3372 -0.6146 0.701 241.248 0.1515 -0.1225 0.1948 321.031 -10.6917

90 -0.0985 -0.4109 0.4225 256.521 0.2476 0.066 0.2563 14.9139 -0.3525 -0.6332 0.7247 240.894 0.1508 -0.1273 0.1973 319.816 -29.9705

95 -0.1249 -0.4262 0.4442 253.663 0.2472 0.0646 0.2555 14.6456 -0.3639 -0.6462 0.7416 240.618 0.1499 -0.1306 0.1988 318.922 -49.1812

100 -0.1487 -0.4368 0.4615 251.199 0.245 0.0635 0.2531 14.5189 -0.3711 -0.6536 0.7516 240.416 0.1487 -0.1325 0.1992 318.29 -67.6524

105 -0.1697 -0.4428 0.4742 249.027 0.2412 0.0624 0.2491 14.5081 -0.3741 -0.6553 0.7545 240.281 0.1473 -0.1332 0.1985 317.874 -84.7612

110 -0.1878 -0.4441 0.4822 247.073 0.2356 0.0613 0.2434 14.5951 -0.3728 -0.6512 0.7503 240.211 0.1454 -0.1326 0.1968 317.641 -99.9306

115 -0.2055 -0.4417 0.4872 245.051 0.2297 0.0578 0.2369 14.1238 -0.3713 -0.6399 0.7398 239.874 0.1405 -0.1279 0.19 317.697 -113.476

120 -0.2172 -0.4333 0.4847 243.372 0.2213 0.0561 0.2283 14.2231 -0.362 -0.6233 0.7208 239.854 0.1371 -0.1242 0.185 317.817 -123.17

125 -0.2248 -0.4194 0.4758 241.804 0.2117 0.0543 0.2186 14.3815 -0.3481 -0.6002 0.6938 239.887 0.1329 -0.1191 0.1785 318.123 -129.242

130 -0.2272 -0.3991 0.4592 240.35 0.2014 0.0526 0.2082 14.6226 -0.3292 -0.5698 0.658 239.981 0.1279 -0.1124 0.1703 318.685 -131.008

135 -0.2222 -0.3705 0.432 239.043 0.1912 0.0513 0.198 15.0047 -0.3045 -0.5308 0.6119 240.156 0.1221 -0.1036 0.1601 319.668 -127.537

140 -0.2064 -0.3303 0.3895 238.005 0.1826 0.0511 0.1896 15.6513 -0.2724 -0.4807 0.5525 240.462 0.1154 -0.0919 0.1475 321.464 -117.357

145 -0.1721 -0.2718 0.3217 237.652 0.1781 0.0538 0.186 16.796 -0.2296 -0.4149 0.4742 241.038 0.108 -0.0754 0.1317 325.078 -97.7931

150 -0.1032 -0.1805 0.2079 240.249 0.1837 0.0625 0.194 18.8035 -0.1691 -0.3233 0.3648 242.382 0.1008 -0.0503 0.1126 333.489 -63.2786

155 0.0431 -0.0206 0.0478 334.427 0.2144 0.0865 0.2312 21.9813 -0.0735 -0.1817 0.196 247.971 0.097 -0.0066 0.0972 356.103 -0.1455

160 0.4082 0.3209 0.5192 38.1773 0.3209 0.1559 0.3568 25.9054 0.111 0.0824 0.1382 36.61 0.111 0.0877 0.1415 38.3165 134.255

165 2.1744 1.7827 2.8118 39.3482 0.928 0.5491 1.0783 30.613 0.8089 1.027 1.3073 51.7755 0.2886 0.4907 0.5693 59.5359 695.253

170 25.1062 17.9851 30.883 35.6164 9.5616 5.7294 11.1468 30.9303 7.8573 9.8546 12.6035 51.4337 3.8518 5.3217 6.5694 54.1034 6716.4

175 19.6345 10.4847 22.259 28.102 8.2578 4.5624 9.4344 28.9207 3.626 3.3627 4.9453 42.8425 4.7372 3.6618 5.9875 37.7039 3699.1

180 2.1513 0.4644 2.2009 12.1822 1.1552 0.5481 1.2787 25.3835 -0.0843 -0.5066 0.5136 260.557 0.9013 0.3123 0.9539 19.1103 141.325

185 0.6164 -0.2574 0.668 337.335 0.4858 0.184 0.5194 20.7421 -0.289 -0.637 0.6995 245.597 0.4863 0.0443 0.4883 5.1994 -94.3851

190 0.1869 -0.4192 0.459 294.035 0.2829 0.0752 0.2928 14.8902 -0.3116 -0.6105 0.6854 242.958 0.3452 -0.0243 0.3461 355.965 -135.496

195 0.0153 -0.4648 0.4651 271.883 0.1927 0.0267 0.1945 7.8982 -0.3025 -0.5654 0.6413 241.854 0.2747 -0.0485 0.2789 349.987 -137.837

200 -0.0644 -0.4741 0.4785 262.27 0.1445 0.0004 0.1445 0.1467 -0.2863 -0.5205 0.594 241.189 0.2313 -0.0578 0.2384 345.959 -128.877

205 -0.1026 -0.4689 0.48 257.654 0.1161 -0.0154 0.1171 352.43 -0.2688 -0.4786 0.5489 240.678 0.2008 -0.0611 0.2099 343.086 -116.111

210 -0.1195 -0.4567 0.4721 255.332 0.0984 -0.0253 0.1016 345.602 -0.2516 -0.4397 0.5066 240.215 0.1772 -0.0614 0.1875 340.893 -102.171

215 -0.1559 -0.4474 0.4738 250.786 0.0618 -0.0452 0.0766 323.833 -0.2265 -0.3869 0.4483 239.656 0.143 -0.0621 0.1559 336.508 -84.3084

220 -0.1502 -0.4284 0.454 250.676 0.0552 -0.0482 0.0732 318.87 -0.2107 -0.3527 0.4109 239.153 0.1269 -0.0596 0.1402 334.829 -70.4793

225 -0.141 -0.4083 0.432 250.946 0.0501 -0.0495 0.0705 315.355 -0.1957 -0.3205 0.3755 238.588 0.1123 -0.0568 0.1258 333.168 -57.511

230 -0.1301 -0.3876 0.4089 251.442 0.0455 -0.0499 0.0675 312.401 -0.1815 -0.2897 0.3418 237.939 0.0986 -0.0538 0.1124 331.366 -45.4833

235 -0.1188 -0.3668 0.3856 252.054 0.0405 -0.0498 0.0642 309.118 -0.1677 -0.26 0.3094 237.179 0.0854 -0.0508 0.0994 329.245 -34.4086

240 -0.1078 -0.3462 0.3626 252.701 0.0344 -0.0499 0.0606 304.608 -0.1543 -0.231 0.2778 236.271 0.0725 -0.0478 0.0868 326.563 -24.2595

245 -0.0977 -0.3261 0.3404 253.32 0.0269 -0.0507 0.0574 297.986 -0.141 -0.2025 0.2468 235.16 0.0594 -0.0448 0.0744 322.955 -14.9881

250 -0.0887 -0.3067 0.3192 253.86 0.0177 -0.0525 0.0554 288.621 -0.1277 -0.1742 0.216 233.757 0.0462 -0.0419 0.0623 317.798 -6.5401

255 -0.081 -0.288 0.2992 254.288 0.0066 -0.0556 0.056 276.75 -0.1142 -0.1457 0.1851 231.903 0.0325 -0.0388 0.0506 309.952 1.1311

260 -0.0745 -0.27 0.2801 254.58 -0.0064 -0.0604 0.0607 263.968 -0.1004 -0.1167 0.1539 229.299 0.0184 -0.0357 0.0401 297.268 8.0502

265 -0.0667 -0.2538 0.2625 255.282 -0.0177 -0.0651 0.0674 254.81 -0.0886 -0.0917 0.1275 225.986 0.0066 -0.0327 0.0334 281.411 13.4817

270 -0.0629 -0.2361 0.2444 255.084 -0.0354 -0.0737 0.0818 244.342 -0.0728 -0.0595 0.094 219.24 -0.0096 -0.0291 0.0306 251.782 19.139

275 -0.0586 -0.2136 0.2215 254.646 -0.0557 -0.0826 0.0996 236.015 -0.0544 -0.0228 0.059 202.77 -0.0244 -0.022 0.0329 221.992 23.443

280 -0.055 -0.1923 0.2 254.036 -0.0759 -0.0924 0.1196 230.586 -0.0368 0.0128 0.039 160.86 -0.0418 -0.0173 0.0452 202.429 26.6465

285 -0.051 -0.1672 0.1749 253.026 -0.0973 -0.1018 0.1409 226.288 -0.0181 0.051 0.0541 109.524 -0.0598 -0.0117 0.0609 191.03 28.1772

290 -0.0465 -0.1365 0.1442 251.194 -0.1199 -0.1099 0.1627 222.507 0.0023 0.0925 0.0925 88.5878 -0.0786 -0.0049 0.0787 183.594 27.5072

295 -0.0411 -0.0977 0.106 247.206 -0.1438 -0.1155 0.1845 218.767 0.0246 0.1384 0.1406 79.915 -0.0982 0.0033 0.0983 178.084 23.89

300 -0.0343 -0.0475 0.0586 234.15 -0.1691 -0.1169 0.2056 214.658 0.0495 0.1901 0.1965 75.4064 -0.1189 0.0135 0.1197 173.527 16.2799

305 -0.0257 0.0184 0.0316 144.46 -0.196 -0.1121 0.2258 209.773 0.0777 0.2497 0.2615 72.7038 -0.1409 0.0263 0.1434 169.41 3.2047

310 -0.0142 0.1062 0.1071 97.6064 -0.2249 -0.0985 0.2455 203.65 0.1106 0.32 0.3386 70.9411 -0.1647 0.0428 0.1702 165.432 -17.4595

315 0.0022 0.2252 0.2252 89.4373 -0.2559 -0.072 0.2659 195.717 0.1498 0.4058 0.4326 69.7344 -0.1912 0.0644 0.2017 161.387 -48.9342

320 0.028 0.3982 0.3992 85.9715 -0.2916 -0.0245 0.2926 184.812 0.2017 0.52 0.5578 68.7987 -0.2215 0.0955 0.2412 156.667 -98.3162

325 0.0694 0.6401 0.6438 83.8108 -0.3277 0.0512 0.3316 171.12 0.2661 0.6671 0.7182 68.2527 -0.2578 0.1366 0.2918 152.087 -171.659

330 0.1464 1.0257 1.0361 81.8788 -0.3659 0.1837 0.4094 153.335 0.3592 0.8853 0.9554 67.9144 -0.3047 0.2001 0.3645 146.704 -292.567

335 0.3885 2.0218 2.0588 79.122 -0.4053 0.5546 0.6869 126.156 0.5691 1.4024 1.5135 67.9109 -0.3955 0.3575 0.5331 137.885 -607.563

340 1.0775 4.325 4.4571 76.011 -0.3464 1.506 1.5453 102.953 0.9736 2.4372 2.6245 68.2249 -0.4993 0.7002 0.86 125.489 -1348.9

345 5.6432 16.9204 17.837 71.5558 0.8988 7.3423 7.3971 83.0206 2.6437 7.0195 7.5008 69.3628 -0.4093 2.4245 2.4588 99.5832 -5417.9

350 269.847 567.771 628.63 64.5795 130.516 316.97 342.789 67.62 30.8311 115.73 119.766 75.0825 58.4842 66.0233 88.2014 48.4651 -184410

355 4.0837 5.4471 6.8079 53.1409 2.8156 4.2611 5.1073 56.5447 -0.6924 -0.9085 1.1422 232.689 1.7491 0.387 1.7914 12.4748 -1759.5

360 0.985 0.5579 1.1321 29.5277 0.7846 0.879 1.1782 48.2453 -0.3966 -0.7862 0.8806 243.234 0.5852 -0.0285 0.5859 357.213 -169.782

Appendix A15


theta2

degree

F12x

/10.^6

N

F12y

/10.^6

N

F12

/10.^6

N

theta12

degree

F14x

/10.^6

N

F14y

/10.^6

N

F14

/10.^6

N

theta14

degree

F16x

/10.^6

N

F16y

/10.^6

N

F16

/10.^6

N

theta16

degree

0 -1.0374 -0.5444 1.1716 207.6919 -1.0374 -0.5444 1.1716 207.6919 0.4826 -0.6646 0.8213 305.9871

5 -0.6302 -0.1372 0.6449 192.2814 -0.6302 -0.1372 0.6449 192.2814 0.2605 -0.408 0.4841 302.5617

10 -0.4915 -0.0696 0.4964 188.065 -0.4915 -0.0696 0.4964 188.065 0.1601 -0.2885 0.3299 299.0244

15 -0.4356 -0.0771 0.4424 190.0417 -0.4356 -0.0771 0.4424 190.0417 0.1089 -0.22 0.2455 296.3336

20 -0.4055 -0.0868 0.4147 192.0762 -0.4055 -0.0868 0.4147 192.0762 0.0785 -0.183 0.1991 293.209

25 -0.3833 -0.0867 0.393 192.7493 -0.3833 -0.0867 0.393 192.7493 0.0607 -0.1629 0.1738 290.4511

30 -0.3605 -0.0735 0.368 191.5272 -0.3605 -0.0735 0.368 191.5272 0.0507 -0.154 0.1622 288.2158

35 -0.3337 -0.0483 0.3372 188.2312 -0.3337 -0.0483 0.3372 188.2312 0.0454 -0.1529 0.1595 286.5509

40 -0.2994 -0.0094 0.2996 181.7951 -0.2994 -0.0094 0.2996 181.7951 0.0407 -0.1601 0.1652 284.2562

45 -0.2629 0.0313 0.2647 173.2196 -0.2629 0.0313 0.2647 173.2196 0.0403 -0.1671 0.1719 283.5616

50 -0.2227 0.0752 0.235 161.3408 -0.2227 0.0752 0.235 161.3408 0.0412 -0.1757 0.1804 283.187

55 -0.18 0.12 0.2164 146.3187 -0.18 0.12 0.2164 146.3187 0.0428 -0.1844 0.1893 283.0531

60 -0.1361 0.1637 0.2129 129.7544 -0.1361 0.1637 0.2129 129.7544 0.0448 -0.1925 0.1976 283.109

65 -0.0921 0.2048 0.2246 114.2111 -0.0921 0.2048 0.2246 114.2111 0.0472 -0.1993 0.2048 283.323

70 -0.0488 0.2425 0.2474 101.3799 -0.0488 0.2425 0.2474 101.3799 0.0497 -0.2044 0.2104 283.6749

75 -0.007 0.276 0.2761 91.4428 -0.007 0.276 0.2761 91.4428 0.0524 -0.2077 0.2142 284.1505

80 0.0287 0.2945 0.2959 84.4255 0.0287 0.2945 0.2959 84.4255 0.0547 -0.209 0.216 284.6759

85 0.0662 0.3181 0.3249 78.2491 0.0662 0.3181 0.3249 78.2491 0.0576 -0.2093 0.2171 285.3769

90 0.1012 0.3374 0.3523 73.3021 0.1012 0.3374 0.3523 73.3021 0.0604 -0.2082 0.2167 286.1779

95 0.1337 0.3525 0.377 69.231 0.1337 0.3525 0.377 69.231 0.0631 -0.2056 0.215 287.0722

100 0.1635 0.3636 0.3986 65.7904 0.1635 0.3636 0.3986 65.7904 0.0657 -0.2017 0.2121 288.0536

105 0.1903 0.3705 0.4166 62.8104 0.1903 0.3705 0.4166 62.8104 0.0681 -0.1966 0.2081 289.1162

110 0.2142 0.3735 0.4306 60.172 0.2142 0.3735 0.4306 60.172 0.0703 -0.1904 0.203 290.2534

115 0.2373 0.3734 0.4424 57.5643 0.2373 0.3734 0.4424 57.5643 0.0696 -0.1801 0.193 291.1213

120 0.2542 0.3678 0.4471 55.3512 0.2542 0.3678 0.4471 55.3512 0.0702 -0.1713 0.1851 292.2887

125 0.2666 0.3573 0.4458 53.2738 0.2666 0.3573 0.4458 53.2738 0.0701 -0.1615 0.176 293.463

130 0.2733 0.3409 0.437 51.284 0.2733 0.3409 0.437 51.284 0.0689 -0.1506 0.1657 294.5953

135 0.2723 0.3168 0.4178 49.3249 0.2723 0.3168 0.4178 49.3249 0.0664 -0.1387 0.1538 295.5908

140 0.2598 0.2816 0.3832 47.3019 0.2598 0.2816 0.3832 47.3019 0.0619 -0.1256 0.1401 296.2463

145 0.2287 0.2286 0.3234 44.9806 0.2287 0.2286 0.3234 44.9806 0.0545 -0.1113 0.1239 296.07

150 0.1631 0.1434 0.2172 41.3206 0.1631 0.1434 0.2172 41.3206 0.0419 -0.0958 0.1045 293.6509

155 0.0225 -0.0095 0.0244 337.1051 0.0225 -0.0095 0.0244 337.1051 0.0199 -0.08 0.0824 283.9485

160 -0.326 -0.3418 0.4723 226.3558 -0.326 -0.3418 0.4723 226.3558 -0.0246 -0.07 0.0742 250.6629

165 -1.9849 -1.7801 2.6662 221.8865 -1.9849 -1.7801 2.6662 221.8865 -0.1747 -0.1405 0.2242 218.812

170 -22.9845 -17.7213 29.0229 217.6326 -22.9845 -17.7213 29.0229 217.6326 -1.3717 -2.2502 2.6353 238.6341

175 -17.1548 -10.2221 19.9695 210.7895 -17.1548 -10.2221 19.9695 210.7895 0.0774 -3.3271 3.328 271.333

180 -1.666 -0.4228 1.7188 194.2391 -1.666 -0.4228 1.7188 194.2391 0.2538 -0.6908 0.736 290.1746

185 -0.3425 0.2833 0.4445 140.4081 -0.3425 0.2833 0.4445 140.4081 0.2222 -0.3837 0.4434 300.0835

190 0.0161 0.4447 0.445 87.9297 0.0161 0.4447 0.445 87.9297 0.2025 -0.2744 0.341 306.4251

195 0.1519 0.4935 0.5163 72.8871 0.1519 0.4935 0.5163 72.8871 0.1899 -0.2174 0.2886 311.1361

200 0.2087 0.507 0.5483 67.6241 0.2087 0.507 0.5483 67.6241 0.1813 -0.181 0.2561 315.0406

205 0.23 0.5063 0.5561 65.5726 0.23 0.5063 0.5561 65.5726 0.175 -0.1548 0.2336 318.507

210 0.2329 0.4987 0.5504 64.9721 0.2329 0.4987 0.5504 64.9721 0.1701 -0.1342 0.2167 321.7142

215 0.2546 0.4937 0.5554 62.7214 0.2546 0.4937 0.5554 62.7214 0.1558 -0.1067 0.1889 325.6013

220 0.2381 0.4788 0.5348 63.5604 0.2381 0.4788 0.5348 63.5604 0.1518 -0.0928 0.1779 328.5487

225 0.2188 0.4626 0.5118 64.687 0.2188 0.4626 0.5118 64.687 0.1478 -0.0805 0.1683 331.4138

230 0.1983 0.4455 0.4876 66.0047 0.1983 0.4455 0.4876 66.0047 0.1435 -0.0693 0.1594 334.2228

235 0.1777 0.4279 0.4633 67.4432 0.1777 0.4279 0.4633 67.4432 0.1388 -0.0589 0.1507 337.0058

240 0.1578 0.41 0.4394 68.949 0.1578 0.41 0.4394 68.949 0.1332 -0.049 0.1419 339.8045

245 0.1391 0.3923 0.4162 70.4804 0.1391 0.3923 0.4162 70.4804 0.1267 -0.0395 0.1327 342.6824

250 0.1217 0.3748 0.3941 72.0062 0.1217 0.3748 0.3941 72.0062 0.119 -0.0302 0.1228 345.739

255 0.1059 0.3576 0.373 73.5046 0.1059 0.3576 0.373 73.5046 0.1099 -0.0211 0.112 349.1344

260 0.0915 0.3406 0.3527 74.9638 0.0915 0.3406 0.3527 74.9638 0.0994 -0.012 0.1001 353.1377

265 0.0762 0.3249 0.3337 76.8086 0.0762 0.3249 0.3337 76.8086 0.0903 -0.0045 0.0904 357.142

270 0.065 0.307 0.3138 78.0509 0.065 0.307 0.3138 78.0509 0.0756 0.0055 0.0758 4.1642

275 0.0536 0.2837 0.2887 79.3007 0.0536 0.2837 0.2887 79.3007 0.0611 0.0188 0.0639 17.1019

280 0.0431 0.261 0.2645 80.6172 0.0431 0.261 0.2645 80.6172 0.043 0.0296 0.0522 34.526

285 0.0326 0.2338 0.2361 82.0569 0.0326 0.2338 0.2361 82.0569 0.0233 0.0411 0.0472 60.4272

290 0.0219 0.2003 0.2015 83.7715 0.0219 0.2003 0.2015 83.7715 0.002 0.0535 0.0536 87.9123

295 0.0106 0.158 0.1583 86.1763 0.0106 0.158 0.1583 86.1763 -0.0211 0.0672 0.0705 107.4102

300 -0.0017 0.1036 0.1036 90.9176 -0.0017 0.1036 0.1036 90.9176 -0.0459 0.0827 0.0946 119.0104

305 -0.0154 0.0327 0.0361 115.2059 -0.0154 0.0327 0.0361 115.2059 -0.0725 0.1004 0.1239 125.8147

310 -0.0316 -0.0609 0.0686 242.597 -0.0316 -0.0609 0.0686 242.597 -0.1012 0.1213 0.158 129.8364

315 -0.0522 -0.1866 0.1938 254.3839 -0.0522 -0.1866 0.1938 254.3839 -0.1325 0.1465 0.1975 132.1257

320 -0.0816 -0.3673 0.3763 257.4699 -0.0816 -0.3673 0.3763 257.4699 -0.1671 0.1801 0.2456 132.8535

325 -0.1259 -0.6181 0.6308 258.4845 -0.1259 -0.6181 0.6308 258.4845 -0.2067 0.2204 0.3022 133.1533

330 -0.2047 -1.0149 1.0353 258.5954 -0.2047 -1.0149 1.0353 258.5954 -0.2542 0.276 0.3752 132.6475

335 -0.4451 -2.0321 2.0803 257.6463 -0.4451 -2.0321 2.0803 257.6463 -0.3355 0.385 0.5107 131.065

340 -1.1227 -4.3725 4.5144 255.5991 -1.1227 -4.3725 4.5144 255.5991 -0.4095 0.5314 0.6709 127.6148

345 -5.5988 -17.1323 18.0239 251.9026 -5.5988 -17.1323 18.0239 251.9026 -0.166 0.6047 0.627 105.3492

350 -264.4894 -573.526 631.5748 245.2426 -264.489 -573.526 631.5748 245.2426 61.0313 -56.3685 83.0796 317.2744

355 -4.0731 -5.4654 6.8163 233.3046 -4.0731 -5.4654 6.8163 233.3046 1.6226 -1.8921 2.4926 310.6152

360 -1.0374 -0.5444 1.1716 207.6919 -1.0374 -0.5444 1.1716 207.6919 0.4826 -0.6646 0.8213 305.9871

Appendix A15


theta2

degree

F32x

/10.^6

N

F32y

/10.^6

N

F32

/10.^6

N

theta32

degree

F43x

/10.^6

N

F43y

/10.^6

N

F43

/10.^6

N

theta43

degree

F53x

/10.^6

N

F53y

/10.^6

N

F53

/10.^6

N

theta53

degree

F65x

/10.^6

N

F65y

/10.^6

N

F65

/10.^6

N

theta65

degree

T/10.^3

N.m

0 0.9611 0.5441 1.1044 29.5141 0.9611 0.5441 1.1044 29.5141 -0.3997 -0.8126 0.9056 243.808 0.582 -0.0551 0.5847 354.59 -165.654

5 0.5542 0.1302 0.5692 13.2177 0.5542 0.1302 0.5692 13.2177 -0.2565 -0.568 0.6232 245.697 0.3525 -0.049 0.3559 352.083 -24.8531

10 0.4164 0.056 0.4202 7.6631 0.4164 0.056 0.4202 7.6631 -0.1782 -0.4203 0.4565 247.016 0.2519 -0.0298 0.2537 353.258 5.1206

15 0.3619 0.057 0.3664 8.9529 0.3619 0.057 0.3664 8.9529 -0.1278 -0.3263 0.3505 248.608 0.2033 -0.0105 0.2036 357.041 11.6546

20 0.3339 0.0603 0.3393 10.238 0.3339 0.0603 0.3393 10.238 -0.0994 -0.2746 0.292 250.1 0.1762 -0.0009 0.1762 359.696 17.4156

25 0.3142 0.0541 0.3188 9.7734 0.3142 0.0541 0.3188 9.7734 -0.0858 -0.2511 0.2654 251.136 0.1619 0.0021 0.1619 0.7584 25.3945

30 0.2945 0.035 0.2966 6.7811 0.2945 0.035 0.2966 6.7811 -0.0842 -0.2494 0.2632 251.343 0.1548 -0.0006 0.1548 359.76 35.4966

35 0.2712 0.0041 0.2713 0.8763 0.2712 0.0041 0.2713 0.8763 -0.0924 -0.2643 0.28 250.72 0.1517 -0.0083 0.152 356.864 46.2319

40 0.241 -0.04 0.2443 350.571 0.241 -0.04 0.2443 350.571 -0.1112 -0.2947 0.315 249.332 0.1483 -0.0228 0.1501 351.256 56.398

45 0.209 -0.0856 0.2258 337.73 0.209 -0.0856 0.2258 337.73 -0.1336 -0.3306 0.3566 248.002 0.1485 -0.0364 0.1529 346.218 63.3067

50 0.1737 -0.134 0.2193 322.342 0.1737 -0.134 0.2193 322.342 -0.1603 -0.3718 0.4049 246.681 0.1491 -0.0512 0.1576 341.064 66.6306

55 0.1363 -0.1828 0.228 306.699 0.1363 -0.1828 0.228 306.699 -0.1896 -0.4154 0.4566 245.471 0.1498 -0.0659 0.1636 336.239 65.8294

60 0.098 -0.2301 0.2501 293.07 0.098 -0.2301 0.2501 293.07 -0.2198 -0.459 0.5089 244.405 0.1504 -0.0799 0.1703 331.999 60.7928

65 0.0599 -0.2744 0.2808 282.31 0.0599 -0.2744 0.2808 282.31 -0.2497 -0.5006 0.5594 243.485 0.1508 -0.0926 0.1769 328.438 51.7555

70 0.0227 -0.3146 0.3154 274.131 0.0227 -0.3146 0.3154 274.131 -0.2781 -0.5389 0.6064 242.701 0.151 -0.1036 0.1831 325.547 39.2032

75 -0.0128 -0.3501 0.3503 267.908 -0.0128 -0.3501 0.3503 267.908 -0.304 -0.5727 0.6484 242.039 0.151 -0.1127 0.1884 323.261 23.7874

80 -0.042 -0.37 0.3724 263.525 -0.042 -0.37 0.3724 263.525 -0.3201 -0.5941 0.6749 241.684 0.1501 -0.1198 0.192 321.398 6.9519

85 -0.0728 -0.3945 0.4011 259.541 -0.0728 -0.3945 0.4011 259.541 -0.3388 -0.6176 0.7045 241.25 0.1498 -0.1258 0.1956 319.99 -11.6215

90 -0.1012 -0.4141 0.4263 256.264 -0.1012 -0.4141 0.4263 256.264 -0.3538 -0.6358 0.7276 240.902 0.1494 -0.1302 0.1982 318.947 -30.8018

95 -0.1271 -0.4289 0.4473 253.5 -0.1271 -0.4289 0.4473 253.5 -0.3649 -0.6484 0.744 240.633 0.1488 -0.1331 0.1996 318.202 -49.8825

100 -0.1502 -0.439 0.464 251.112 -0.1502 -0.439 0.464 251.112 -0.3718 -0.6555 0.7536 240.435 0.148 -0.1346 0.2 317.701 -68.1992

105 -0.1706 -0.4446 0.4762 249.007 -0.1706 -0.4446 0.4762 249.007 -0.3746 -0.6568 0.7561 240.305 0.1467 -0.1349 0.1993 317.402 -85.135

110 -0.1881 -0.4456 0.4836 247.116 -0.1881 -0.4456 0.4836 247.116 -0.3731 -0.6524 0.7516 240.239 0.1451 -0.134 0.1975 317.273 -100.118

115 -0.205 -0.4429 0.488 245.158 -0.205 -0.4429 0.488 245.158 -0.3714 -0.6408 0.7407 239.904 0.1404 -0.129 0.1907 317.425 -113.462

120 -0.216 -0.4342 0.485 243.548 -0.216 -0.4342 0.485 243.548 -0.3619 -0.624 0.7213 239.887 0.1372 -0.1251 0.1856 317.63 -122.957

125 -0.2228 -0.4202 0.4756 242.061 -0.2228 -0.4202 0.4756 242.061 -0.3479 -0.6006 0.6941 239.922 0.1331 -0.1198 0.1791 318.012 -128.83

130 -0.2243 -0.3997 0.4584 240.707 -0.2243 -0.3997 0.4584 240.707 -0.3289 -0.57 0.6581 240.016 0.1282 -0.1129 0.1709 318.639 -130.409

135 -0.2183 -0.3711 0.4306 239.532 -0.2183 -0.3711 0.4306 239.532 -0.3041 -0.5308 0.6118 240.189 0.1224 -0.1039 0.1606 319.671 -126.775

140 -0.2014 -0.331 0.3875 238.682 -0.2014 -0.331 0.3875 238.682 -0.2721 -0.4807 0.5523 240.491 0.1157 -0.0921 0.1478 321.487 -116.483

145 -0.1662 -0.2727 0.3194 238.633 -0.1662 -0.2727 0.3194 238.633 -0.2294 -0.4149 0.4741 241.058 0.1082 -0.0756 0.1319 325.06 -96.9149

150 -0.0971 -0.1819 0.2062 241.919 -0.0971 -0.1819 0.2062 241.919 -0.1692 -0.3235 0.3651 242.386 0.1007 -0.0507 0.1127 333.262 -62.6292

155 0.0467 -0.0231 0.0521 333.641 0.0467 -0.0231 0.0521 333.641 -0.0742 -0.1828 0.1973 247.919 0.0963 -0.008 0.0967 355.269 -0.2907

160 0.3977 0.3153 0.5075 38.4123 0.3977 0.3153 0.5075 38.4123 0.1093 0.0783 0.1344 35.615 0.1093 0.0833 0.1374 37.3228 131.643

165 2.0586 1.76 2.7084 40.5289 2.0586 1.76 2.7084 40.5289 0.8048 1.0053 1.2878 51.3203 0.2846 0.4688 0.5484 58.7415 679.538

170 23.0596 17.7076 29.074 37.5209 23.0596 17.7076 29.0742 37.5209 7.8638 9.5629 12.3809 50.5686 3.8583 5.0298 6.3392 52.5086 6525.2

175 17.2308 10.2151 20.031 30.661 17.2308 10.2151 20.0312 30.661 3.6952 3.0792 4.81 39.8038 4.8064 3.3781 5.8748 35.1005 3553.7

180 1.7423 0.4224 1.7928 13.6278 1.7423 0.4224 1.7928 13.6278 -0.0643 -0.5479 0.5517 263.309 0.9213 0.2708 0.9603 16.3787 128.633

185 0.4185 -0.277 0.5019 326.5 0.4185 -0.277 0.5019 326.5 -0.2759 -0.6542 0.71 247.137 0.4994 0.0268 0.5002 3.0733 -94.9827

190 0.059 -0.4318 0.4358 277.787 0.059 -0.4318 0.4358 277.787 -0.3011 -0.6202 0.6894 244.1 0.3557 -0.0342 0.3573 354.5 -132.428

195 -0.0783 -0.4741 0.4805 260.628 -0.0783 -0.4741 0.4805 260.628 -0.2934 -0.5716 0.6425 242.825 0.2837 -0.0549 0.289 349.058 -133.103

200 -0.137 -0.4813 0.5004 254.106 -0.137 -0.4813 0.5004 254.106 -0.2782 -0.5246 0.5938 242.065 0.2394 -0.0621 0.2473 345.451 -123.274

205 -0.1608 -0.4744 0.501 251.274 -0.1608 -0.4744 0.501 251.274 -0.2614 -0.4813 0.5477 241.492 0.2082 -0.064 0.2178 342.916 -110.08

210 -0.1668 -0.461 0.4902 250.108 -0.1668 -0.461 0.4902 250.108 -0.2449 -0.4414 0.5048 240.981 0.184 -0.0633 0.1946 341.007 -96.0171

215 -0.1921 -0.4503 0.4895 246.898 -0.1921 -0.4503 0.4895 246.898 -0.2205 -0.3875 0.4459 240.362 0.1489 -0.063 0.1617 337.066 -78.6371

220 -0.1797 -0.4302 0.4662 247.331 -0.1797 -0.4302 0.4662 247.331 -0.2052 -0.3529 0.4082 239.823 0.1323 -0.06 0.1453 335.624 -65.0617

225 -0.1649 -0.4091 0.441 248.048 -0.1649 -0.4091 0.441 248.048 -0.1907 -0.3202 0.3727 239.22 0.1173 -0.0567 0.1303 334.187 -52.4763

230 -0.1493 -0.3874 0.4152 248.929 -0.1493 -0.3874 0.4152 248.929 -0.1769 -0.2891 0.3389 238.53 0.1031 -0.0534 0.1162 332.61 -40.9258

235 -0.134 -0.3657 0.3895 249.883 -0.134 -0.3657 0.3895 249.883 -0.1637 -0.2591 0.3065 237.724 0.0895 -0.0502 0.1026 330.725 -30.389

240 -0.1197 -0.3444 0.3646 250.835 -0.1197 -0.3444 0.3646 250.835 -0.1507 -0.2299 0.2749 236.766 0.076 -0.0469 0.0894 328.31 -20.8075

245 -0.1068 -0.3236 0.3407 251.727 -0.1068 -0.3236 0.3407 251.727 -0.1378 -0.2013 0.2439 235.598 0.0626 -0.0438 0.0764 325.021 -12.1053

250 -0.0957 -0.3035 0.3182 252.508 -0.0957 -0.3035 0.3182 252.508 -0.1249 -0.1728 0.2132 234.129 0.0489 -0.0406 0.0636 320.27 -4.2053

255 -0.0862 -0.2843 0.2971 253.141 -0.0862 -0.2843 0.2971 253.141 -0.1118 -0.1441 0.1824 232.194 0.0349 -0.0375 0.0512 312.947 2.9569

260 -0.0783 -0.2659 0.2771 253.599 -0.0783 -0.2659 0.2771 253.599 -0.0983 -0.115 0.1513 229.478 0.0204 -0.0342 0.0399 300.821 9.4178

265 -0.0695 -0.2493 0.2588 254.421 -0.0695 -0.2493 0.2588 254.421 -0.0868 -0.09 0.125 226.016 0.0084 -0.0312 0.0323 284.989 14.4663

270 -0.065 -0.2311 0.2401 254.297 -0.065 -0.2311 0.2401 254.297 -0.0713 -0.0576 0.0917 218.94 -0.0081 -0.0275 0.0286 253.597 19.771

275 -0.0602 -0.2081 0.2166 253.852 -0.0602 -0.2081 0.2166 253.852 -0.0531 -0.0209 0.0571 201.448 -0.0232 -0.0203 0.0308 221.152 23.7746

280 -0.0564 -0.1862 0.1946 253.16 -0.0564 -0.1862 0.1946 253.16 -0.0358 0.0149 0.0387 157.399 -0.0407 -0.0154 0.0435 200.682 26.718

285 -0.0524 -0.1605 0.1689 251.932 -0.0524 -0.1605 0.1689 251.932 -0.0171 0.0532 0.0559 107.835 -0.0589 -0.0096 0.0597 189.282 28.0121

290 -0.048 -0.129 0.1377 249.612 -0.048 -0.129 0.1377 249.612 0.0031 0.0949 0.095 88.1116 -0.0777 -0.0027 0.0778 182.006 27.1089

295 -0.0428 -0.0892 0.099 244.376 -0.0428 -0.0892 0.099 244.376 0.0254 0.141 0.1433 79.7893 -0.0974 0.0057 0.0976 176.656 23.2383

300 -0.0365 -0.0379 0.0526 226.067 -0.0365 -0.0379 0.0526 226.067 0.0503 0.193 0.1994 75.4014 -0.1181 0.0161 0.1192 172.233 15.3287

305 -0.0284 0.0295 0.0409 133.936 -0.0284 0.0295 0.0409 133.936 0.0785 0.2528 0.2647 72.7435 -0.1402 0.0292 0.1432 168.229 1.8795

310 -0.0175 0.119 0.1203 98.345 -0.0175 0.119 0.1203 98.345 0.1114 0.3233 0.342 70.9942 -0.1639 0.0459 0.1702 164.349 -19.2643

315 -0.0018 0.2402 0.2402 90.4249 -0.0018 0.2402 0.2402 90.4249 0.1507 0.4094 0.4363 69.7849 -0.1902 0.0678 0.202 160.395 -51.3617

320 0.0232 0.416 0.4166 86.8082 0.0232 0.416 0.4166 86.8082 0.2028 0.5239 0.5618 68.837 -0.2204 0.0992 0.2417 155.763 -101.572

325 0.0634 0.6615 0.6645 84.5217 0.0634 0.6615 0.6645 84.5217 0.2675 0.6712 0.7226 68.2695 -0.2564 0.1405 0.2924 151.279 -176.032

330 0.1387 1.0526 1.0617 82.496 0.1387 1.0526 1.0617 82.496 0.3612 0.8895 0.9601 67.8997 -0.3027 0.2042 0.3651 146.002 -298.581

335 0.3759 2.064 2.0979 79.6774 0.3759 2.064 2.0979 79.6774 0.5729 1.406 1.5182 67.8303 -0.3917 0.3609 0.5326 137.342 -617.647

340 1.0511 4.3983 4.5221 76.5599 1.0511 4.3983 4.5221 76.5599 0.9815 2.4361 2.6264 68.0551 -0.4913 0.699 0.8544 125.104 -1367.2

345 5.5252 17.1517 18.02 72.1444 5.5252 17.1517 18.0196 72.1444 2.6743 6.9707 7.4661 69.0107 -0.3787 2.3755 2.4055 99.0579 -5476.7

350 264.414 573.539 631.56 65.2492 264.414 573.539 631.555 65.2492 31.7372 111.685 116.107 74.1367 59.3903 61.979 85.8405 46.2219 -185850

355 3.9971 5.4717 6.7762 53.8515 3.9971 5.4717 6.7762 53.8515 -0.6887 -0.9922 1.2078 235.237 1.7528 0.303 1.7788 9.8083 -1764.8

360 0.9611 0.5441 1.1044 29.5141 0.9611 0.5441 1.1044 29.5141 -0.3997 -0.8126 0.9056 243.808 0.582 -0.0551 0.5847 354.59 -165.654

Appendix A16


theta2

degree

F12x

/10.^6

N

F12y

/10.^6

N

F12

/10.^6

N

theta12

degree

F14x

/10.^6

N

F14y

/10.^6

N

F14

/10.^6

N

theta14

degree

F16x

/10.^6

N

F16y

/10.^6

N

F16

/10.^6

N

theta16

degree

0 -1.0618 -0.5597 1.2003 207.7958 0.9941 -0.5483 1.1353 331.1212 0.4859 -0.6378 0.8018 307.3048

5 -0.6459 -0.154 0.664 193.4138 0.4874 -0.2661 0.5553 331.3718 0.2644 -0.3903 0.4714 304.1141

10 -0.5043 -0.0862 0.5117 189.7023 0.3005 -0.1418 0.3322 334.7388 0.1642 -0.2747 0.32 300.8655

15 -0.4473 -0.0935 0.4569 191.8068 0.2157 -0.0756 0.2285 340.6836 0.1132 -0.2081 0.2369 298.5416

20 -0.4167 -0.1029 0.4292 193.8682 0.1743 -0.0433 0.1796 346.034 0.0829 -0.1721 0.191 295.7168

25 -0.3942 -0.1025 0.4073 194.569 0.1535 -0.031 0.1566 348.5765 0.0653 -0.1527 0.1661 293.1456

30 -0.3712 -0.0887 0.3817 193.4344 0.1433 -0.0313 0.1467 347.6895 0.0553 -0.1444 0.1546 290.9437

35 -0.3441 -0.0626 0.3497 190.3141 0.1389 -0.0391 0.1443 344.2878 0.05 -0.1438 0.1523 289.1706

40 -0.3093 -0.0228 0.3102 184.2073 0.138 -0.052 0.1475 339.3677 0.0451 -0.1515 0.1581 286.5859

45 -0.2723 0.019 0.2729 176.0159 0.1393 -0.0651 0.1538 334.9518 0.0446 -0.1592 0.1653 285.6565

50 -0.2314 0.064 0.2401 164.534 0.1423 -0.0781 0.1623 331.2432 0.0452 -0.1683 0.1743 285.0406

55 -0.1881 0.11 0.2179 149.6933 0.1466 -0.09 0.172 328.4695 0.0465 -0.1777 0.1837 284.6787

60 -0.1435 0.1547 0.2111 132.8467 0.1519 -0.1001 0.182 326.6061 0.0483 -0.1864 0.1925 284.5282

65 -0.0988 0.1969 0.2203 116.6376 0.1578 -0.1084 0.1915 325.5232 0.0503 -0.1938 0.2002 284.5594

70 -0.0548 0.2356 0.2419 103.0952 0.1641 -0.1146 0.2001 325.0692 0.0525 -0.1995 0.2063 284.7508

75 -0.0123 0.2699 0.2702 92.6027 0.1703 -0.1188 0.2076 325.1065 0.0548 -0.2034 0.2106 285.0853

80 0.0241 0.2891 0.2902 85.2353 0.1726 -0.1153 0.2076 326.2663 0.0569 -0.2051 0.2128 285.4918

85 0.0622 0.3134 0.3195 78.7832 0.1773 -0.1145 0.211 327.1337 0.0594 -0.2059 0.2143 286.0805

90 0.0978 0.3333 0.3474 73.6477 0.181 -0.1121 0.2129 328.2301 0.0619 -0.2052 0.2143 286.7808

95 0.1309 0.349 0.3727 69.443 0.1835 -0.1081 0.213 329.5 0.0643 -0.203 0.2129 287.5838

100 0.1612 0.3604 0.3948 65.9025 0.1846 -0.1027 0.2112 330.9022 0.0667 -0.1994 0.2103 288.4818

105 0.1887 0.3678 0.4133 62.8427 0.184 -0.0962 0.2076 332.4082 0.0688 -0.1947 0.2065 289.4676

110 0.2131 0.3711 0.4279 60.1351 0.1816 -0.0886 0.202 334.0001 0.0707 -0.1888 0.2016 290.5335

115 0.2368 0.3712 0.4403 57.4621 0.1786 -0.0825 0.1967 335.2175 0.0698 -0.1788 0.1919 291.3318

120 0.2544 0.3658 0.4456 55.1823 0.1725 -0.0737 0.1876 336.8606 0.0703 -0.1702 0.1842 292.4367

125 0.2676 0.3555 0.445 53.0304 0.1642 -0.0644 0.1764 338.5796 0.07 -0.1606 0.1753 293.5544

130 0.2752 0.3392 0.4368 50.9516 0.1538 -0.0547 0.1633 340.4155 0.0688 -0.15 0.165 294.6386

135 0.2751 0.3151 0.4183 48.879 0.1414 -0.0447 0.1483 342.4594 0.0662 -0.1383 0.1533 295.6005

140 0.2637 0.2798 0.3845 46.7003 0.1273 -0.0343 0.1318 344.9091 0.0618 -0.1253 0.1397 296.251

145 0.2335 0.2265 0.3253 44.1384 0.1126 -0.0235 0.1151 348.1989 0.0544 -0.1109 0.1236 296.1324

150 0.1681 0.1409 0.2193 39.9739 0.1004 -0.012 0.1012 353.2046 0.0422 -0.0951 0.1041 293.9242

155 0.0248 -0.0132 0.0281 332.0417 0.1008 0.0012 0.1008 0.6638 0.0207 -0.0784 0.0811 284.7835

160 -0.3378 -0.3486 0.4854 225.9052 0.1542 0.0178 0.1552 6.5814 -0.0227 -0.0655 0.0693 250.8908

165 -2.1019 -1.8041 2.77 220.6397 0.6589 0.0553 0.6613 4.7972 -0.1704 -0.1184 0.2076 214.7933

170 -25.0324 -18 30.8321 215.7188 10.0977 0.0042 10.0977 0.0239 -1.378 -1.9581 2.3944 234.864

175 -19.5598 -10.493 22.1966 208.2117 11.9191 -0.6121 11.9348 357.0603 0.0084 -3.0432 3.0432 270.1573

180 -2.0763 -0.4661 2.128 192.6534 2.1057 -0.165 2.1121 355.5201 0.234 -0.6491 0.69 289.824

185 -0.5418 0.2623 0.6019 154.1639 1.0653 -0.0984 1.0699 354.722 0.2093 -0.366 0.4216 299.76

190 -0.1131 0.4306 0.4453 104.718 0.7238 -0.0731 0.7274 354.2323 0.1922 -0.2643 0.3268 306.0211

195 0.0571 0.4828 0.4861 83.2532 0.5612 -0.0604 0.5644 353.8599 0.181 -0.2108 0.2778 310.6438

200 0.1348 0.4984 0.5163 74.8672 0.4676 -0.0532 0.4706 353.5065 0.1733 -0.1765 0.2474 314.4746

205 0.1705 0.4992 0.5276 71.1405 0.4068 -0.049 0.4097 353.1278 0.1678 -0.1517 0.2262 317.8847

210 0.1844 0.493 0.5263 69.4882 0.3635 -0.0465 0.3665 352.7058 0.1635 -0.1321 0.2102 321.0524

215 0.2173 0.4892 0.5353 66.0555 0.2937 -0.0395 0.2963 352.3359 0.15 -0.1056 0.1835 324.853

220 0.2075 0.4755 0.5188 66.4188 0.2697 -0.0389 0.2725 351.8011 0.1465 -0.0923 0.1731 327.7846

225 0.1939 0.4603 0.4994 67.1555 0.2488 -0.0385 0.2517 351.1996 0.143 -0.0804 0.164 330.6446

230 0.1782 0.4441 0.4785 68.139 0.2293 -0.0383 0.2325 350.5062 0.1392 -0.0695 0.1556 333.4559

235 0.1616 0.4273 0.4568 69.2832 0.2104 -0.0383 0.2138 349.6814 0.1349 -0.0594 0.1474 336.2443

240 0.1451 0.4102 0.4351 70.5263 0.1913 -0.0383 0.1951 348.6664 0.1298 -0.0497 0.139 339.0478

245 0.1291 0.3932 0.4138 71.8227 0.1718 -0.0385 0.1761 347.3746 0.1237 -0.0404 0.1301 341.9253

250 0.114 0.3763 0.3932 73.1405 0.1517 -0.0387 0.1566 345.6769 0.1164 -0.0313 0.1205 344.9713

255 0.1 0.3596 0.3733 74.4586 0.1311 -0.0391 0.1368 343.3751 0.1077 -0.0222 0.11 348.34

260 0.087 0.343 0.3539 75.767 0.11 -0.0397 0.1169 340.1531 0.0975 -0.0132 0.0984 352.2932

265 0.0727 0.3277 0.3357 77.4974 0.0923 -0.0424 0.1016 335.311 0.0887 -0.0058 0.0889 356.2494

270 0.0623 0.3103 0.3165 78.651 0.0693 -0.0428 0.0814 328.287 0.0742 0.0041 0.0743 3.1453

275 0.0514 0.2875 0.292 79.8583 0.0454 -0.0425 0.0623 316.8918 0.0599 0.0172 0.0624 16.0454

280 0.0412 0.2653 0.2685 81.1683 0.0232 -0.0426 0.0485 298.579 0.0421 0.0279 0.0505 33.5553

285 0.0308 0.2388 0.2408 82.6522 0.0014 -0.0421 0.0421 271.8545 0.0225 0.0392 0.0452 60.1598

290 0.0199 0.2061 0.207 84.4775 -0.0202 -0.0405 0.0453 243.5558 0.0013 0.0515 0.0515 88.6083

295 0.0084 0.1647 0.1649 87.0933 -0.0414 -0.0373 0.0557 221.9808 -0.0217 0.065 0.0686 108.4684

300 -0.0042 0.1114 0.1115 92.1814 -0.0625 -0.0315 0.07 206.7625 -0.0465 0.0803 0.0928 120.0638

305 -0.0185 0.0419 0.0458 113.7551 -0.0833 -0.0222 0.0862 194.9311 -0.0731 0.0978 0.1221 126.7787

310 -0.0353 -0.0499 0.0611 234.7461 -0.1034 -0.0081 0.1037 184.4572 -0.1019 0.1184 0.1562 130.7078

315 -0.0566 -0.1734 0.1824 251.939 -0.1219 0.0125 0.1225 174.1526 -0.1333 0.1433 0.1957 132.9164

320 -0.0869 -0.3514 0.362 256.11 -0.1385 0.0434 0.1452 162.616 -0.168 0.1766 0.2438 133.5733

325 -0.1323 -0.5985 0.6129 257.5333 -0.1437 0.0826 0.1657 150.1021 -0.2079 0.2167 0.3004 133.8142

330 -0.2128 -0.9897 1.0123 257.8624 -0.1263 0.1355 0.1852 132.9916 -0.256 0.2721 0.3736 133.2543

335 -0.4581 -1.9917 2.0437 257.0466 0.0088 0.2146 0.2148 87.6465 -0.3391 0.3818 0.5107 131.6068

340 -1.1496 -4.3009 4.4519 255.0353 0.5071 0.2776 0.5781 28.6945 -0.4173 0.5329 0.6768 128.0618

345 -5.7173 -16.9027 17.8434 251.3119 4.3747 -0.1516 4.3773 358.0148 -0.1965 0.6539 0.6828 106.7239

350 -269.9221 -567.7595 628.6563 244.5728 261.6404 -76.3648 272.557 343.7291 60.1254 -52.3239 79.7048 318.9687

355 -4.1602 -5.4423 6.8503 232.6052 4.3469 -1.9715 4.7731 335.6043 1.6191 -1.808 2.427 311.8448

360 -1.0618 -0.5597 1.2003 207.7958 0.9941 -0.5483 1.1353 331.1212 0.4859 -0.6378 0.8018 307.3048

Appendix A16


theta2

degree

F32x

/10.^6

N

F32y

/10.^6

N

F32

/10.^6

N

theta32

degree

F43x

/10.^6

N

F43y

/10.^6

N

F43

/10.^6

N

theta43

degree

F53x

/10.^6

N

F53y

/10.^6

N

F53

/10.^6

N

theta53

degree

F65x

/10.^6

N

F65y

/10.^6

N

F65

/10.^6

N

theta65

degree

T/10.^3

N.m

0 0.9855 0.5594 1.1332 29.5778 0.785 0.8794 1.1788 48.2449 -0.3964 -0.7858 0.8801 243.23 -0.3964 -0.7858 0.8801 243.23 -170.309

5 0.5699 0.147 0.5885 14.465 0.4369 0.4605 0.6348 46.5106 -0.2526 -0.5503 0.6055 245.342 -0.2526 -0.5503 0.6055 245.342 -29.5443

10 0.4292 0.0726 0.4353 9.6015 0.3033 0.3221 0.4424 46.72 -0.1741 -0.4065 0.4422 246.81 -0.1741 -0.4065 0.4422 246.81 0.8285

15 0.3736 0.0734 0.3807 11.1121 0.2431 0.2637 0.3586 47.3215 -0.1235 -0.3144 0.3378 248.548 -0.1235 -0.3144 0.3378 248.548 7.7646

20 0.345 0.0764 0.3534 12.488 0.2158 0.2294 0.3149 46.7451 -0.095 -0.2637 0.2803 250.195 -0.095 -0.2637 0.2803 250.195 13.9699

25 0.3251 0.0698 0.3325 12.126 0.2044 0.204 0.2887 44.9472 -0.0813 -0.2409 0.2543 251.36 -0.0813 -0.2409 0.2543 251.36 22.459

30 0.3051 0.0502 0.3092 9.3337 0.201 0.1819 0.2711 42.1545 -0.0796 -0.2397 0.2526 251.628 -0.0796 -0.2397 0.2526 251.628 33.1292

35 0.2816 0.0185 0.2822 3.7563 0.2018 0.1617 0.2586 38.7169 -0.0879 -0.2551 0.2699 250.994 -0.0879 -0.2551 0.2699 250.994 44.4617

40 0.2509 -0.0267 0.2523 353.937 0.2049 0.1422 0.2495 34.759 -0.1067 -0.2862 0.3054 249.547 -0.1067 -0.2862 0.3054 249.547 55.2178

45 0.2183 -0.0733 0.2303 341.446 0.2094 0.126 0.2443 31.0308 -0.1293 -0.3226 0.3476 248.165 -0.1293 -0.3226 0.3476 248.165 62.6766

50 0.1824 -0.1228 0.2199 326.04 0.2146 0.1119 0.242 27.5376 -0.1562 -0.3644 0.3965 246.799 -0.1562 -0.3644 0.3965 246.799 66.4861

55 0.1444 -0.1728 0.2252 309.873 0.2204 0.1001 0.242 24.4223 -0.1858 -0.4087 0.4489 245.554 -0.1858 -0.4087 0.4489 245.554 66.0918

60 0.1054 -0.2212 0.245 295.477 0.2263 0.0903 0.2437 21.7481 -0.2164 -0.4529 0.5019 244.462 -0.2164 -0.4529 0.5019 244.462 61.3781

65 0.0665 -0.2665 0.2746 284.023 0.2322 0.0823 0.2463 19.5178 -0.2466 -0.4951 0.5531 243.523 -0.2466 -0.4951 0.5531 243.523 52.581

70 0.0287 -0.3076 0.309 275.331 0.2377 0.0758 0.2495 17.6979 -0.2753 -0.534 0.6008 242.724 -0.2753 -0.534 0.6008 242.724 40.1924

75 -0.0075 -0.344 0.3441 268.756 0.2425 0.0706 0.2526 16.2384 -0.3016 -0.5684 0.6434 242.05 -0.3016 -0.5684 0.6434 242.05 24.8718

80 -0.0373 -0.3646 0.3666 264.152 0.2446 0.07 0.2544 15.9682 -0.318 -0.5903 0.6705 241.687 -0.318 -0.5903 0.6705 241.687 8.0599

85 -0.0688 -0.3898 0.3958 259.99 0.247 0.0676 0.2561 15.3068 -0.3371 -0.6142 0.7006 241.245 -0.3371 -0.6142 0.7006 241.245 -10.5277

90 -0.0978 -0.41 0.4215 256.583 0.2481 0.0659 0.2567 14.8639 -0.3524 -0.6328 0.7243 240.891 -0.3524 -0.6328 0.7243 240.891 -29.7622

95 -0.1242 -0.4253 0.4431 253.719 0.2477 0.0645 0.256 14.5964 -0.3637 -0.6459 0.7412 240.616 -0.3637 -0.6459 0.7412 240.616 -48.9292

100 -0.148 -0.4359 0.4603 251.252 0.2457 0.0634 0.2537 14.4702 -0.3709 -0.6532 0.7512 240.413 -0.3709 -0.6532 0.7512 240.413 -67.3576

105 -0.1689 -0.4418 0.473 249.077 0.2418 0.0624 0.2497 14.4596 -0.3739 -0.6549 0.7541 240.278 -0.3739 -0.6549 0.7541 240.278 -84.4249

110 -0.187 -0.4431 0.481 247.122 0.2363 0.0613 0.2441 14.5463 -0.3726 -0.6508 0.7499 240.208 -0.3726 -0.6508 0.7499 240.208 -99.5549

115 -0.2046 -0.4407 0.4859 245.098 0.2305 0.0578 0.2376 14.0767 -0.3711 -0.6395 0.7394 239.871 -0.3711 -0.6395 0.7394 239.871 -113.063

120 -0.2163 -0.4323 0.4834 243.419 0.2221 0.0561 0.2291 14.1756 -0.3618 -0.6229 0.7204 239.851 -0.3618 -0.6229 0.7204 239.851 -122.724

125 -0.2238 -0.4184 0.4745 241.851 0.2125 0.0543 0.2194 14.3335 -0.3479 -0.5998 0.6934 239.884 -0.3479 -0.5998 0.6934 239.884 -128.764

130 -0.2261 -0.398 0.4578 240.398 0.2023 0.0526 0.209 14.5737 -0.329 -0.5694 0.6576 239.978 -0.329 -0.5694 0.6576 239.978 -130.504

135 -0.2212 -0.3694 0.4306 239.094 0.1921 0.0513 0.1989 14.9546 -0.3043 -0.5304 0.6115 240.153 -0.3043 -0.5304 0.6115 240.153 -127.01

140 -0.2052 -0.3292 0.3879 238.06 0.1835 0.0512 0.1905 15.5995 -0.2722 -0.4803 0.5521 240.459 -0.2722 -0.4803 0.5521 240.459 -116.812

145 -0.171 -0.2707 0.3202 237.721 0.1791 0.0539 0.187 16.7412 -0.2294 -0.4145 0.4738 241.035 -0.2294 -0.4145 0.4738 241.035 -97.2353

150 -0.102 -0.1794 0.2064 240.381 0.1847 0.0627 0.195 18.7447 -0.169 -0.3229 0.3644 242.379 -0.169 -0.3229 0.3644 242.379 -62.7128

155 0.0443 -0.0195 0.0484 336.312 0.2155 0.0867 0.2322 21.9212 -0.0733 -0.1813 0.1956 247.977 -0.0733 -0.1813 0.1956 247.977 0.4228

160 0.4094 0.3221 0.521 38.1951 0.322 0.1561 0.3579 25.8571 0.1111 0.0828 0.1386 36.693 0.1111 0.0828 0.1386 36.693 134.82

165 2.1756 1.784 2.8135 39.3514 0.9291 0.5493 1.0794 30.5942 0.8091 1.0274 1.3077 51.7798 0.8091 1.0274 1.3077 51.7798 695.811

170 25.1075 17.9864 30.885 35.6169 9.5627 5.7296 11.1478 30.9285 7.8575 9.8549 12.604 51.4342 7.8575 9.8549 12.604 51.4342 6716.9

175 19.6358 10.486 22.26 28.1033 8.2589 4.5627 9.4355 28.919 3.6262 3.3631 4.9457 42.8444 3.6262 3.3631 4.9457 42.8444 3699.6

180 2.1526 0.4658 2.2024 12.2092 1.1564 0.5485 1.2798 25.3748 -0.0841 -0.5062 0.5132 260.569 -0.0841 -0.5062 0.5132 260.569 141.828

185 0.6178 -0.256 0.6687 337.487 0.4869 0.1843 0.5206 20.7345 -0.2888 -0.6366 0.6991 245.597 -0.2888 -0.6366 0.6991 245.597 -93.909

190 0.1882 -0.4178 0.4582 294.256 0.2841 0.0756 0.294 14.9066 -0.3115 -0.6101 0.685 242.957 -0.3115 -0.6101 0.685 242.957 -135.051

195 0.0166 -0.4634 0.4637 272.048 0.1938 0.0271 0.1957 7.9742 -0.3023 -0.5651 0.6408 241.852 -0.3023 -0.5651 0.6408 241.852 -137.424

200 -0.0631 -0.4727 0.4769 262.396 0.1456 0.0008 0.1456 0.3201 -0.2861 -0.5201 0.5936 241.185 -0.2861 -0.5201 0.5936 241.185 -128.5

205 -0.1014 -0.4674 0.4782 257.759 0.1172 -0.015 0.1181 352.723 -0.2686 -0.4782 0.5484 240.673 -0.2686 -0.4782 0.5484 240.673 -115.771

210 -0.1184 -0.4552 0.4703 255.424 0.0994 -0.0248 0.1024 346.01 -0.2515 -0.4393 0.5062 240.209 -0.2515 -0.4393 0.5062 240.209 -101.869

215 -0.1548 -0.4459 0.4719 250.857 0.0628 -0.0447 0.077 324.581 -0.2263 -0.3865 0.4478 239.65 -0.2263 -0.3865 0.4478 239.65 -84.0465

220 -0.1491 -0.4268 0.4521 250.743 0.0561 -0.0476 0.0736 319.67 -0.2105 -0.3523 0.4104 239.145 -0.2105 -0.3523 0.4104 239.145 -70.2572

225 -0.14 -0.4067 0.4301 251.01 0.051 -0.049 0.0707 316.187 -0.1956 -0.3201 0.3751 238.578 -0.1956 -0.3201 0.3751 238.578 -57.329

230 -0.1291 -0.386 0.407 251.504 0.0464 -0.0493 0.0677 313.257 -0.1813 -0.2893 0.3414 237.927 -0.1813 -0.2893 0.3414 237.927 -45.3416

235 -0.1178 -0.3652 0.3837 252.114 0.0413 -0.0492 0.0642 309.998 -0.1675 -0.2596 0.309 237.164 -0.1675 -0.2596 0.309 237.164 -34.3074

240 -0.1069 -0.3445 0.3608 252.76 0.0352 -0.0493 0.0606 305.509 -0.1541 -0.2306 0.2774 236.252 -0.1541 -0.2306 0.2774 236.252 -24.1991

245 -0.0969 -0.3244 0.3386 253.376 0.0276 -0.05 0.0571 298.886 -0.1408 -0.2021 0.2463 235.137 -0.1408 -0.2021 0.2463 235.137 -14.9685

250 -0.0879 -0.305 0.3174 253.914 0.0183 -0.0518 0.055 289.461 -0.1275 -0.1738 0.2155 233.727 -0.1275 -0.1738 0.2155 233.727 -6.5616

255 -0.0803 -0.2863 0.2974 254.339 0.0072 -0.055 0.0555 277.433 -0.114 -0.1452 0.1847 231.864 -0.114 -0.1452 0.1847 231.864 1.0682

260 -0.0738 -0.2683 0.2783 254.626 -0.0058 -0.0597 0.06 264.418 -0.1002 -0.1163 0.1535 229.243 -0.1002 -0.1163 0.1535 229.243 7.9457

265 -0.066 -0.2521 0.2606 255.325 -0.0172 -0.0644 0.0667 255.071 -0.0884 -0.0913 0.1271 225.908 -0.0884 -0.0913 0.1271 225.908 13.3369

270 -0.0623 -0.2344 0.2425 255.12 -0.0349 -0.073 0.0809 244.425 -0.0726 -0.059 0.0936 219.105 -0.0726 -0.059 0.0936 219.105 18.9519

275 -0.0581 -0.2118 0.2197 254.671 -0.0552 -0.0819 0.0987 235.994 -0.0542 -0.0224 0.0587 202.455 -0.0542 -0.0224 0.0587 202.455 23.2134

280 -0.0545 -0.1905 0.1982 254.048 -0.0755 -0.0917 0.1188 230.515 -0.0367 0.0132 0.039 160.21 -0.0367 0.0132 0.039 160.21 26.3746

285 -0.0505 -0.1655 0.173 253.019 -0.097 -0.1011 0.1401 226.192 -0.0179 0.0514 0.0544 109.228 -0.0179 0.0514 0.0544 109.228 27.8632

290 -0.046 -0.1348 0.1424 251.148 -0.1196 -0.1092 0.162 222.397 0.0024 0.0929 0.0929 88.5018 0.0024 0.0929 0.0929 88.5018 27.1516

295 -0.0406 -0.0959 0.1042 247.06 -0.1435 -0.1148 0.1837 218.648 0.0248 0.1388 0.141 79.8852 0.0248 0.1388 0.141 79.8852 23.4935

300 -0.0339 -0.0457 0.0569 233.453 -0.1688 -0.1162 0.2049 214.532 0.0497 0.1906 0.1969 75.3955 0.0497 0.1906 0.1969 75.3955 15.8435

305 -0.0253 0.0202 0.0324 141.425 -0.1957 -0.1114 0.2252 209.641 0.0779 0.2501 0.262 72.7004 0.0779 0.2501 0.262 72.7004 2.7301

310 -0.0138 0.108 0.1088 97.2639 -0.2246 -0.0977 0.2449 203.512 0.1107 0.3204 0.339 70.9409 0.1107 0.3204 0.339 70.9409 -17.9701

315 0.0026 0.227 0.227 89.3383 -0.2557 -0.0713 0.2654 195.574 0.15 0.4062 0.433 69.7356 0.15 0.4062 0.433 69.7356 -49.4776

320 0.0285 0.4 0.401 85.9312 -0.2913 -0.0238 0.2923 184.669 0.2019 0.5205 0.5582 68.8003 0.2019 0.5205 0.5582 68.8003 -98.8885

325 0.0698 0.6418 0.6456 83.7913 -0.3274 0.0519 0.3315 170.985 0.2662 0.6675 0.7186 68.2543 0.2662 0.6675 0.7186 68.2543 -172.255

330 0.1468 1.0274 1.0379 81.8694 -0.3656 0.1845 0.4095 153.226 0.3594 0.8857 0.9558 67.9157 0.3594 0.8857 0.9558 67.9157 -293.179

335 0.389 2.0235 2.0606 79.119 -0.405 0.5553 0.6873 126.102 0.5693 1.4028 1.5139 67.9117 0.5693 1.4028 1.5139 67.9117 -608.183

340 1.0779 4.3266 4.4589 76.0105 -0.3461 1.5066 1.5458 102.937 0.9737 2.4376 2.6249 68.2254 0.9737 2.4376 2.6249 68.2254 -1349.5

345 5.6436 16.922 17.838 71.5561 0.8992 7.3429 7.3978 83.0186 2.6438 7.0199 7.5012 69.3629 2.6438 7.0199 7.5012 69.3629 -5418.5

350 269.847 567.772 628.64 64.5795 130.516 316.97 342.79 67.62 30.8313 115.73 119.766 75.0825 30.8313 115.73 119.766 75.0825 -184410

355 4.0842 5.4486 6.8094 53.1452 2.8159 4.2615 5.1078 56.5445 -0.6922 -0.9081 1.1418 232.682 -0.6922 -0.9081 1.1418 232.682 -1760.1

360 0.9855 0.5594 1.1332 29.5778 0.785 0.8794 1.1788 48.2449 -0.3964 -0.7858 0.8801 243.23 -0.3964 -0.7858 0.8801 243.23 -170.309

Appendix A17


theta2

degree

F12x

/10.^5

N

F12y

/10.^5

N

F12

/10.^5

N

theta12

degree

F14x

/10.^5

N

F14y

/10.^5

N

F14

/10.^5

N

theta14

degree

F16x

/10.^5

N

F16y

/10.^5

N

F16

/10.^5

N

theta16

degree

0 6.1054 27.0076 27.6891 77.2618 2.9634 -8.1104 8.6348 290.0713 4.1237 -5.7045 7.039 305.8627

5 4.3437 16.902 17.4513 75.5872 1.4908 -4.7773 5.0045 287.3316 2.5282 -3.7619 4.5325 303.9038

10 3.4683 11.9882 12.4798 73.8642 0.8566 -3.1869 3.3 285.0456 1.7235 -2.7528 3.2478 302.0504

15 2.943 9.1916 9.6512 72.246 0.5337 -2.2589 2.3211 283.293 1.3043 -2.1517 2.5161 301.2226

20 2.6707 7.626 8.0801 70.6994 0.3632 -1.7062 1.7445 282.0174 1.0526 -1.8332 2.1139 299.8638

25 2.576 6.7964 7.2682 69.2419 0.2691 -1.3647 1.391 281.1534 0.9106 -1.676 1.9074 298.5151

30 2.6254 6.4587 6.9719 67.8788 0.2156 -1.1511 1.1711 280.6071 0.8359 -1.6306 1.8324 297.1412

35 2.7923 6.4581 7.036 66.6175 0.1847 -1.0138 1.0305 280.3265 0.8037 -1.6635 1.8475 295.7876

40 3.0764 6.7289 7.3988 65.4302 0.1682 -0.9309 0.946 280.239 0.773 -1.7803 1.9409 293.4706

45 3.4042 7.1018 7.8756 64.3894 0.1595 -0.8588 0.8735 280.5215 0.7843 -1.895 2.0509 292.4824

50 3.776 7.5592 8.4498 63.4569 0.1568 -0.7975 0.8128 281.122 0.8065 -2.0224 2.1773 291.7404

55 4.1695 8.0529 9.0683 62.6264 0.158 -0.7408 0.7574 282.0385 0.8359 -2.1487 2.3056 291.2573

60 4.5651 8.5462 9.6891 61.8902 0.1614 -0.6856 0.7043 283.2504 0.8703 -2.2638 2.4253 291.0285

65 4.9458 9.0115 10.2795 61.2406 0.1658 -0.6307 0.6521 284.7259 0.9082 -2.361 2.5297 291.0397

70 5.2977 9.4288 10.8152 60.6699 0.1698 -0.5758 0.6003 286.4288 0.9487 -2.4368 2.615 291.272

75 5.6099 9.784 11.2782 60.1712 0.1725 -0.5209 0.5487 288.3241 0.991 -2.4897 2.6797 291.7046

80 5.8174 9.8406 11.4315 59.41 0.1349 -0.3317 0.3581 292.1342 1.0302 -2.5264 2.7283 292.1845

85 6.0349 10.0315 11.7068 58.9692 0.1213 -0.2558 0.2831 295.3619 1.0762 -2.5433 2.7617 292.9357

90 6.1999 10.1502 11.8939 58.5827 0.1031 -0.1833 0.2103 299.368 1.1225 -2.5414 2.7782 293.8299

95 6.3097 10.1954 11.9899 58.2476 0.0806 -0.1152 0.1406 304.9678 1.168 -2.5219 2.7793 294.8497

100 6.3624 10.1667 11.9935 57.9614 0.0538 -0.0526 0.0753 315.675 1.2115 -2.4864 2.7658 295.9786

105 6.3569 10.0642 11.9037 57.7221 0.0233 0.0038 0.0236 9.363 1.2519 -2.4359 2.7387 297.2012

110 6.2923 9.8876 11.72 57.5279 -0.0104 0.0535 0.0545 100.9659 1.2877 -2.3714 2.6984 298.5032

115 6.2056 9.6453 11.4691 57.2437 -0.0237 0.0588 0.0634 111.9219 1.2776 -2.2447 2.5828 299.6469

120 6.0246 9.3158 11.0941 57.1088 -0.0546 0.087 0.1027 122.1009 1.2891 -2.1437 2.5014 301.0199

125 5.781 8.9052 10.6171 57.0093 -0.0848 0.1068 0.1364 128.4387 1.2881 -2.0277 2.4022 302.4252

130 5.471 8.4059 10.0296 56.9417 -0.1132 0.1184 0.1638 133.7105 1.2712 -1.8953 2.2821 303.8518

135 5.0873 7.8042 9.3159 56.9011 -0.1385 0.1221 0.1846 138.6136 1.234 -1.7435 2.136 305.2907

140 4.6155 7.0749 8.4473 56.8804 -0.1588 0.1183 0.198 143.3273 1.1696 -1.5669 1.9552 306.7389

145 4.0272 6.1712 7.369 56.8727 -0.1701 0.1077 0.2014 147.6696 1.0668 -1.3552 1.7247 308.2099

150 3.2609 5.0006 5.9698 56.8918 -0.1618 0.0912 0.1857 150.5974 0.9053 -1.0874 1.4149 309.7802

155 2.167 3.358 3.9965 57.1652 -0.0979 0.0695 0.1201 144.6298 0.6424 -0.7161 0.962 311.8972

160 0.295 0.7014 0.7609 67.1924 0.1718 0.0429 0.177 14.022 0.1676 -0.1099 0.2004 326.7431

165 -5.718 -6.6565 8.7752 229.3369 1.9768 0.0526 1.9775 1.5232 -1.2259 1.6375 2.0455 126.8197

170 -58.0918 -42.8871 72.2078 216.4371 36.1441 -0.012 36.1441 359.981 -8.1403 12.8212 15.1871 122.4117

175 -16.3402 42.6503 45.6733 110.9629 44.7048 -0.6311 44.7093 359.1912 9.1758 -4.4674 10.2055 334.0402

180 4.0372 20.2342 20.633 78.7163 8.1424 -0.2266 8.1455 358.4062 4.3833 -3.4428 5.5737 321.8525

185 4.2508 14.613 15.2187 73.7807 4.2735 -0.1832 4.2774 357.5448 3.2833 -2.6212 4.2013 321.3982

190 3.7852 11.9483 12.5336 72.4218 3.0351 -0.1835 3.0406 356.5397 2.758 -2.1859 3.5192 321.6014

195 3.2899 10.2731 10.7871 72.2428 2.464 -0.1954 2.4717 355.4663 2.4316 -1.8919 3.0809 322.1154

200 2.8417 9.0607 9.4959 72.587 2.1422 -0.2118 2.1526 354.3525 2.1942 -1.6704 2.7577 322.7183

205 2.446 8.1024 8.4636 73.2016 1.9317 -0.23 1.9454 353.2093 2.0029 -1.4914 2.4972 323.3275

210 2.0975 7.2979 7.5933 73.9648 1.7749 -0.2483 1.7922 352.0375 1.8374 -1.3396 2.2739 323.9043

215 1.6743 6.1378 6.3621 74.7418 1.5311 -0.2178 1.5465 351.9045 1.5762 -1.1383 1.9442 324.1629

220 1.4078 5.5177 5.6945 75.687 1.4217 -0.2306 1.4403 350.7852 1.4362 -1.0213 1.7623 324.5837

225 1.1737 4.9451 5.0825 76.6482 1.3149 -0.2408 1.3368 349.623 1.3014 -0.9142 1.5904 324.9128

230 0.9675 4.4052 4.5102 77.6125 1.2067 -0.2475 1.2318 348.4092 1.1689 -0.8145 1.4247 325.1313

235 0.7854 3.8863 3.9649 78.575 1.0947 -0.2499 1.1228 347.1395 1.0363 -0.7199 1.2619 325.2129

240 0.624 3.3793 3.4364 79.5377 0.9774 -0.2471 1.0082 345.812 0.9019 -0.6288 1.0995 325.1173

245 0.4808 2.8764 2.9163 80.5107 0.8539 -0.238 0.8864 344.425 0.7641 -0.5395 0.9354 324.7761

250 0.3535 2.3705 2.3968 81.5178 0.7231 -0.2214 0.7562 342.9733 0.6217 -0.4507 0.7679 324.0599

255 0.2405 1.8554 1.871 82.6147 0.5842 -0.1961 0.6162 341.4432 0.4736 -0.361 0.5955 322.6825

260 0.1402 1.3249 1.3323 83.9581 0.4362 -0.1605 0.4648 339.7967 0.3188 -0.269 0.4172 319.8426

265 0.067 0.8773 0.8798 85.6337 0.3047 -0.129 0.3309 337.0503 0.1864 -0.1902 0.2663 314.4145

270 -0.0174 0.2659 0.2664 93.7374 0.1288 -0.0616 0.1428 334.4265 0.0079 -0.0848 0.0852 275.3286

275 -0.0979 -0.413 0.4244 256.6693 -0.0706 0.0281 0.076 158.3079 -0.1596 0.0568 0.1694 160.4045

280 -0.1631 -1.0965 1.1086 261.5409 -0.2706 0.131 0.3006 154.1775 -0.3543 0.1776 0.3963 153.3785

285 -0.2221 -1.8315 1.845 263.0865 -0.4847 0.2569 0.5486 152.0709 -0.5582 0.3096 0.6383 150.988

290 -0.2778 -2.6324 2.6471 263.9769 -0.7145 0.4113 0.8244 150.072 -0.7728 0.4561 0.8974 149.4521

295 -0.3341 -3.5183 3.5341 264.5759 -0.9619 0.6009 1.1342 148.0067 -1.0001 0.6213 1.1773 148.1479

300 -0.3966 -4.5148 4.5322 264.9796 -1.2294 0.8349 1.4861 145.8193 -1.243 0.8109 1.4841 146.8798

305 -0.4735 -5.6581 5.6779 265.2165 -1.5201 1.1256 1.8914 143.4813 -1.5062 1.0327 1.8263 145.5644

310 -0.5768 -7.0007 7.0244 265.2903 -1.8384 1.49 2.3664 140.9749 -1.7973 1.2982 2.2171 144.159

315 -0.725 -8.6231 8.6536 265.1938 -2.1915 1.9532 2.9356 138.2902 -2.1284 1.625 2.6778 142.6392

320 -0.9622 -10.7579 10.8008 264.889 -2.6217 2.5845 3.6815 135.4099 -2.5161 2.0733 3.2603 140.5103

325 -1.3115 -13.4225 13.4864 264.4196 -3.0879 3.3852 4.582 132.3706 -3.0104 2.6274 3.9957 138.8863

330 -1.8904 -17.2116 17.3152 263.7321 -3.6803 4.5188 5.8279 129.161 -3.6903 3.4317 5.0394 137.0795

335 -3.3561 -25.4836 25.7037 262.4976 -4.7817 6.9275 8.4175 124.6156 -5.2042 5.2141 7.3669 134.9457

340 -6.1138 -39.5429 40.0127 261.211 -6.5285 10.7457 12.5734 121.2806 -7.7513 8.4035 11.4325 132.6883

345 -16.0986 -84.0074 85.536 259.1517 -11.1177 21.3651 24.0846 117.4909 -16.1155 19.3106 25.1517 129.8463

350 7.368 676.0042 676.0444 89.3755 191.6463 -346.7825 396.2151 298.9268 79.7439 -50.4469 94.3609 327.6821

355 11.9711 66.2595 67.3322 79.7588 9.4862 -21.6853 23.6694 293.6269 10.2924 -12.824 16.4435 308.75

360 6.1054 27.0076 27.6891 77.2618 2.9634 -8.1104 8.6348 290.0713 4.1237 -5.7045 7.039 305.8627

Appendix A17


theta2

degree

F32x

/10.^5

N

F32y

/10.^5

N

F32

/10.^5

N

theta32

degree

F43x

/10.^5

N

F43y

/10.^5

N

F43

/10.^5

N

theta43

degree

F53x

/10.^5

N

F53y

/10.^5

N

F53

/10.^5

N

theta53

degree

F65x

/10.^5

N

F65y

/10.^5

N

F65

/10.^5

N

theta65

degree

T/10.^3

N.m

0 -6.1054 -27.008 27.689 257.262 2.9634 -8.1104 8.6348 290.071 2.9634 -8.1104 8.6348 290.071 4.1237 -5.7045 7.039 305.863 821.841

5 -4.3437 -16.902 17.451 255.587 1.4908 -4.7773 5.0045 287.332 1.4908 -4.7773 5.0045 287.332 2.5282 -3.7619 4.5325 303.904 500.852

10 -3.4683 -11.988 12.48 253.864 0.8566 -3.1869 3.3 285.046 0.8566 -3.1869 3.3 285.046 1.7235 -2.7528 3.2478 302.05 340.932

15 -2.943 -9.1916 9.6512 252.246 0.5337 -2.2589 2.3211 283.293 0.5337 -2.2589 2.3211 283.293 1.3043 -2.1517 2.5161 301.223 246.991

20 -2.6707 -7.626 8.0801 250.699 0.3632 -1.7062 1.7445 282.017 0.3632 -1.7062 1.7445 282.017 1.0526 -1.8332 2.1139 299.864 190.269

25 -2.576 -6.7964 7.2682 249.242 0.2691 -1.3647 1.391 281.153 0.2691 -1.3647 1.391 281.153 0.9106 -1.676 1.9074 298.515 154.309

30 -2.6254 -6.4587 6.9719 247.879 0.2156 -1.1511 1.1711 280.607 0.2156 -1.1511 1.1711 280.607 0.8359 -1.6306 1.8324 297.141 130.262

35 -2.7923 -6.4581 7.036 246.618 0.1847 -1.0138 1.0305 280.327 0.1847 -1.0138 1.0305 280.327 0.8037 -1.6635 1.8475 295.788 112.243

40 -3.0764 -6.7289 7.3988 245.43 0.1682 -0.9309 0.946 280.239 0.1682 -0.9309 0.946 280.239 0.773 -1.7803 1.9409 293.471 96.6798

45 -3.4042 -7.1018 7.8756 244.389 0.1595 -0.8588 0.8735 280.522 0.1595 -0.8588 0.8735 280.522 0.7843 -1.895 2.0509 292.482 79.5617

50 -3.776 -7.5592 8.4498 243.457 0.1568 -0.7975 0.8128 281.122 0.1568 -0.7975 0.8128 281.122 0.8065 -2.0224 2.1773 291.74 59.8372

55 -4.1695 -8.0529 9.0683 242.626 0.158 -0.7408 0.7574 282.039 0.158 -0.7408 0.7574 282.039 0.8359 -2.1487 2.3056 291.257 36.622

60 -4.5651 -8.5462 9.6891 241.89 0.1614 -0.6856 0.7043 283.25 0.1614 -0.6856 0.7043 283.25 0.8703 -2.2638 2.4253 291.029 9.7252

65 -4.9458 -9.0115 10.28 241.241 0.1658 -0.6307 0.6521 284.726 0.1658 -0.6307 0.6521 284.726 0.9082 -2.361 2.5297 291.04 -20.5099

70 -5.2977 -9.4288 10.815 240.67 0.1698 -0.5758 0.6003 286.429 0.1698 -0.5758 0.6003 286.429 0.9487 -2.4368 2.615 291.272 -53.3556

75 -5.6099 -9.784 11.278 240.171 0.1725 -0.5209 0.5487 288.324 0.1725 -0.5209 0.5487 288.324 0.991 -2.4897 2.6797 291.705 -87.8345

80 -5.8174 -9.8406 11.432 239.41 0.1349 -0.3317 0.3581 292.134 0.1349 -0.3317 0.3581 292.134 1.0302 -2.5264 2.7283 292.185 -122.335

85 -6.0349 -10.032 11.707 238.969 0.1213 -0.2558 0.2831 295.362 0.1213 -0.2558 0.2831 295.362 1.0762 -2.5433 2.7617 292.936 -156.337

90 -6.1999 -10.15 11.894 238.583 0.1031 -0.1833 0.2103 299.368 0.1031 -0.1833 0.2103 299.368 1.1225 -2.5414 2.7782 293.83 -188.663

95 -6.3097 -10.195 11.99 238.248 0.0806 -0.1152 0.1406 304.968 0.0806 -0.1152 0.1406 304.968 1.168 -2.5219 2.7793 294.85 -218.314

100 -6.3624 -10.167 11.994 237.961 0.0538 -0.0526 0.0753 315.675 0.0538 -0.0526 0.0753 315.675 1.2115 -2.4864 2.7658 295.979 -244.39

105 -6.3569 -10.064 11.904 237.722 0.0233 0.0038 0.0236 9.363 0.0233 0.0038 0.0236 9.363 1.2519 -2.4359 2.7387 297.201 -266.113

110 -6.2923 -9.8876 11.72 237.528 -0.0104 0.0535 0.0545 100.966 -0.0104 0.0535 0.0545 100.966 1.2877 -2.3714 2.6984 298.503 -282.836

115 -6.2056 -9.6453 11.469 237.244 -0.0237 0.0588 0.0634 111.922 -0.0237 0.0588 0.0634 111.922 1.2776 -2.2447 2.5828 299.647 -295.184

120 -6.0246 -9.3158 11.094 237.109 -0.0546 0.087 0.1027 122.101 -0.0546 0.087 0.1027 122.101 1.2891 -2.1437 2.5014 301.02 -300.507

125 -5.781 -8.9052 10.617 237.009 -0.0848 0.1068 0.1364 128.439 -0.0848 0.1068 0.1364 128.439 1.2881 -2.0277 2.4022 302.425 -299.534

130 -5.471 -8.4059 10.03 236.942 -0.1132 0.1184 0.1638 133.711 -0.1132 0.1184 0.1638 133.711 1.2712 -1.8953 2.2821 303.852 -291.955

135 -5.0873 -7.8042 9.3159 236.901 -0.1385 0.1221 0.1846 138.614 -0.1385 0.1221 0.1846 138.614 1.234 -1.7435 2.136 305.291 -277.389

140 -4.6155 -7.0749 8.4473 236.88 -0.1588 0.1183 0.198 143.327 -0.1588 0.1183 0.198 143.327 1.1696 -1.5669 1.9552 306.739 -255.2

145 -4.0272 -6.1712 7.369 236.873 -0.1701 0.1077 0.2014 147.67 -0.1701 0.1077 0.2014 147.67 1.0668 -1.3552 1.7247 308.21 -224.119

150 -3.2609 -5.0006 5.9698 236.892 -0.1618 0.0912 0.1857 150.597 -0.1618 0.0912 0.1857 150.597 0.9053 -1.0874 1.4149 309.78 -181.395

155 -2.167 -3.358 3.9965 237.165 -0.0979 0.0695 0.1201 144.63 -0.0979 0.0695 0.1201 144.63 0.6424 -0.7161 0.962 311.897 -120.479

160 -0.295 -0.7014 0.7609 247.192 0.1718 0.0429 0.177 14.022 0.1718 0.0429 0.177 14.022 0.1676 -0.1099 0.2004 326.743 -23.1277

165 5.718 6.6565 8.7752 49.3369 1.9768 0.0526 1.9775 1.5232 1.9768 0.0526 1.9775 1.5232 -1.2259 1.6375 2.0455 126.82 240.688

170 58.0918 42.8871 72.208 36.4371 36.1441 -0.012 36.1441 359.981 36.1441 -0.012 36.1441 359.981 -8.1403 12.8212 15.1871 122.412 1592.2

175 16.3402 -42.65 45.673 290.963 44.7048 -0.6311 44.7093 359.191 44.7048 -0.6311 44.7093 359.191 9.1758 -4.4674 10.2055 334.04 -1249.6

180 -4.0372 -20.234 20.633 258.716 8.1424 -0.2266 8.1455 358.406 8.1424 -0.2266 8.1455 358.406 4.3833 -3.4428 5.5737 321.853 -615.726

185 -4.2508 -14.613 15.219 253.781 4.2735 -0.1832 4.2774 357.545 4.2735 -0.1832 4.2774 357.545 3.2833 -2.6212 4.2013 321.398 -431.708

190 -3.7852 -11.948 12.534 252.422 3.0351 -0.1835 3.0406 356.54 3.0351 -0.1835 3.0406 356.54 2.758 -2.1859 3.5192 321.601 -338.062

195 -3.2899 -10.273 10.787 252.243 2.464 -0.1954 2.4717 355.466 2.464 -0.1954 2.4717 355.466 2.4316 -1.8919 3.0809 322.115 -276.049

200 -2.8417 -9.0607 9.4959 252.587 2.1422 -0.2118 2.1526 354.353 2.1422 -0.2118 2.1526 354.353 2.1942 -1.6704 2.7577 322.718 -229.514

205 -2.446 -8.1024 8.4636 253.202 1.9317 -0.23 1.9454 353.209 1.9317 -0.23 1.9454 353.209 2.0029 -1.4914 2.4972 323.328 -191.999

210 -2.0975 -7.2979 7.5933 253.965 1.7749 -0.2483 1.7922 352.038 1.7749 -0.2483 1.7922 352.038 1.8374 -1.3396 2.2739 323.904 -160.409

215 -1.6743 -6.1378 6.3621 254.742 1.5311 -0.2178 1.5465 351.905 1.5311 -0.2178 1.5465 351.905 1.5762 -1.1383 1.9442 324.163 -123.773

220 -1.4078 -5.5177 5.6945 255.687 1.4217 -0.2306 1.4403 350.785 1.4217 -0.2306 1.4403 350.785 1.4362 -1.0213 1.7623 324.584 -101.086

225 -1.1737 -4.9451 5.0825 256.648 1.3149 -0.2408 1.3368 349.623 1.3149 -0.2408 1.3368 349.623 1.3014 -0.9142 1.5904 324.913 -81.1511

230 -0.9675 -4.4052 4.5102 257.613 1.2067 -0.2475 1.2318 348.409 1.2067 -0.2475 1.2318 348.409 1.1689 -0.8145 1.4247 325.131 -63.6113

235 -0.7854 -3.8863 3.9649 258.575 1.0947 -0.2499 1.1228 347.14 1.0947 -0.2499 1.1228 347.14 1.0363 -0.7199 1.2619 325.213 -48.2542

240 -0.624 -3.3793 3.4364 259.538 0.9774 -0.2471 1.0082 345.812 0.9774 -0.2471 1.0082 345.812 0.9019 -0.6288 1.0995 325.117 -34.9713

245 -0.4808 -2.8764 2.9163 260.511 0.8539 -0.238 0.8864 344.425 0.8539 -0.238 0.8864 344.425 0.7641 -0.5395 0.9354 324.776 -23.7312

250 -0.3535 -2.3705 2.3968 261.518 0.7231 -0.2214 0.7562 342.973 0.7231 -0.2214 0.7562 342.973 0.6217 -0.4507 0.7679 324.06 -14.5627

255 -0.2405 -1.8554 1.871 262.615 0.5842 -0.1961 0.6162 341.443 0.5842 -0.1961 0.6162 341.443 0.4736 -0.361 0.5955 322.683 -7.5443

260 -0.1402 -1.3249 1.3323 263.958 0.4362 -0.1605 0.4648 339.797 0.4362 -0.1605 0.4648 339.797 0.3188 -0.269 0.4172 319.843 -2.7985

265 -0.067 -0.8773 0.8798 265.634 0.3047 -0.129 0.3309 337.05 0.3047 -0.129 0.3309 337.05 0.1864 -0.1902 0.2663 314.415 -0.2961

270 0.0174 -0.2659 0.2664 273.737 0.1288 -0.0616 0.1428 334.427 0.1288 -0.0616 0.1428 334.427 0.0079 -0.0848 0.0852 275.329 -0.5285

275 0.0979 0.413 0.4244 76.6693 -0.0706 0.0281 0.076 158.308 -0.0706 0.0281 0.076 158.308 -0.1596 0.0568 0.1694 160.405 -4.0619

280 0.1631 1.0965 1.1086 81.5409 -0.2706 0.131 0.3006 154.178 -0.2706 0.131 0.3006 154.178 -0.3543 0.1776 0.3963 153.379 -10.6814

285 0.2221 1.8315 1.845 83.0865 -0.4847 0.2569 0.5486 152.071 -0.4847 0.2569 0.5486 152.071 -0.5582 0.3096 0.6383 150.988 -20.9526

290 0.2778 2.6324 2.6471 83.9769 -0.7145 0.4113 0.8244 150.072 -0.7145 0.4113 0.8244 150.072 -0.7728 0.4561 0.8974 149.452 -35.3399

295 0.3341 3.5183 3.5341 84.5759 -0.9619 0.6009 1.1342 148.007 -0.9619 0.6009 1.1342 148.007 -1.0001 0.6213 1.1773 148.148 -54.4592

300 0.3966 4.5148 4.5322 84.9796 -1.2294 0.8349 1.4861 145.819 -1.2294 0.8349 1.4861 145.819 -1.243 0.8109 1.4841 146.88 -79.1449

305 0.4735 5.6581 5.6779 85.2165 -1.5201 1.1256 1.8914 143.481 -1.5201 1.1256 1.8914 143.481 -1.5062 1.0327 1.8263 145.564 -110.559

310 0.5768 7.0007 7.0244 85.2903 -1.8384 1.49 2.3664 140.975 -1.8384 1.49 2.3664 140.975 -1.7973 1.2982 2.2171 144.159 -150.379

315 0.725 8.6231 8.6536 85.1938 -2.1915 1.9532 2.9356 138.29 -2.1915 1.9532 2.9356 138.29 -2.1284 1.625 2.6778 142.639 -201.147

320 0.9622 10.7579 10.801 84.889 -2.6217 2.5845 3.6815 135.41 -2.6217 2.5845 3.6815 135.41 -2.5161 2.0733 3.2603 140.51 -269.595

325 1.3115 13.4225 13.486 84.4196 -3.0879 3.3852 4.582 132.371 -3.0879 3.3852 4.582 132.371 -3.0104 2.6274 3.9957 138.886 -357.47

330 1.8904 17.2116 17.315 83.7321 -3.6803 4.5188 5.8279 129.161 -3.6803 4.5188 5.8279 129.161 -3.6903 3.4317 5.0394 137.08 -482.344

335 3.3561 25.4836 25.704 82.4976 -4.7817 6.9275 8.4175 124.616 -4.7817 6.9275 8.4175 124.616 -5.2042 5.2141 7.3669 134.946 -745.972

340 6.1138 39.5429 40.013 81.211 -6.5285 10.7457 12.5734 121.281 -6.5285 10.7457 12.5734 121.281 -7.7513 8.4035 11.4325 132.688 -1194.4

345 16.0986 84.0074 85.536 79.1517 -11.118 21.3651 24.0846 117.491 -11.1177 21.3651 24.0846 117.491 -16.116 19.3106 25.1517 129.846 -2596

350 -7.368 -676 676.04 269.376 191.646 -346.78 396.215 298.927 191.646 -346.783 396.215 298.927 79.7439 -50.447 94.3609 327.682 20297

355 -11.971 -66.26 67.332 259.759 9.4862 -21.685 23.6694 293.627 9.4862 -21.6853 23.6694 293.627 10.2924 -12.824 16.4435 308.75 2040.4

360 -6.1054 -27.008 27.689 257.262 2.9634 -8.1104 8.6348 290.071 2.9634 -8.1104 8.6348 290.071 4.1237 -5.7045 7.039 305.863 821.841

Appendix A18


theta2

degree

F12x

/10.^7

N

F12y

/10.^7

N

F12

/10.^7

N

theta12

degree

F14x

/10.^7

N

F14y

/10.^7

N

F14

/10.^7

N

theta14

degree

F16x

/10.^7

N

F16y

/10.^7

N

F16

/10.^7

N

theta16

degree

0 -0.2109 -0.1908 0.2844 222.1323 0.1678 -0.0703 0.1819 337.2586 0.0729 -0.0926 0.1179 308.2133

5 -0.1304 -0.0848 0.1555 213.0426 0.0822 -0.031 0.0878 339.3342 0.0389 -0.0556 0.0678 304.9404

10 -0.102 -0.0563 0.1165 208.8695 0.0509 -0.0141 0.0529 344.4996 0.0237 -0.0387 0.0454 301.5501

15 -0.09 -0.048 0.1019 208.0632 0.0369 -0.0055 0.0373 351.543 0.016 -0.0291 0.0332 298.7919

20 -0.0836 -0.0444 0.0946 207.973 0.0301 -0.0016 0.0301 357.0007 0.0114 -0.0238 0.0264 295.6754

25 -0.0792 -0.0415 0.0894 207.6567 0.0267 -0.0005 0.0267 358.8826 0.0088 -0.0209 0.0227 292.7976

30 -0.0753 -0.0379 0.0843 206.7301 0.025 -0.0013 0.0251 357.0561 0.0073 -0.0196 0.0209 290.3148

35 -0.071 -0.0332 0.0784 205.0887 0.0243 -0.0032 0.0245 352.6241 0.0064 -0.0194 0.0205 288.3168

40 -0.0658 -0.0272 0.0712 202.4411 0.0242 -0.0057 0.0249 346.7711 0.0058 -0.0203 0.0211 285.889

45 -0.0603 -0.0209 0.0638 199.1607 0.0245 -0.0083 0.0258 341.2506 0.0056 -0.0213 0.0221 284.8286

50 -0.0542 -0.0144 0.0561 194.8644 0.025 -0.0108 0.0272 336.5233 0.0057 -0.0226 0.0233 284.1087

55 -0.0478 -0.0078 0.0484 189.2792 0.0257 -0.0132 0.0289 332.8681 0.0058 -0.0239 0.0246 283.6554

60 -0.0412 -0.0014 0.0412 181.9856 0.0266 -0.0152 0.0306 330.2711 0.006 -0.0251 0.0258 283.4166

65 -0.0344 0.0046 0.0347 172.4105 0.0276 -0.0169 0.0324 328.5879 0.0062 -0.0261 0.0268 283.3568

70 -0.0277 0.0101 0.0295 159.959 0.0287 -0.0182 0.034 327.644 0.0064 -0.0269 0.0277 283.451

75 -0.0212 0.0151 0.026 144.5122 0.0298 -0.0191 0.0354 327.2789 0.0067 -0.0275 0.0283 283.6809

80 -0.0154 0.0184 0.0239 129.9042 0.0303 -0.0192 0.0358 327.6886 0.0069 -0.0277 0.0285 283.9931

85 -0.0093 0.0221 0.024 112.7853 0.0311 -0.0193 0.0366 328.216 0.0072 -0.0278 0.0287 284.4688

90 -0.0035 0.0253 0.0255 97.7768 0.0318 -0.0191 0.0371 329.019 0.0074 -0.0277 0.0287 285.0502

95 0.0021 0.0279 0.028 85.7002 0.0323 -0.0186 0.0373 330.0336 0.0077 -0.0274 0.0285 285.7296

100 0.0074 0.0301 0.031 76.2629 0.0326 -0.0179 0.0372 331.2121 0.008 -0.0269 0.0281 286.5011

105 0.0123 0.0318 0.0341 68.8396 0.0326 -0.0169 0.0367 332.5203 0.0082 -0.0262 0.0275 287.359

110 0.0169 0.033 0.037 62.8672 0.0322 -0.0158 0.0359 333.9358 0.0084 -0.0254 0.0268 288.2977

115 0.0214 0.0338 0.04 57.6141 0.0317 -0.0147 0.0349 335.1295 0.0083 -0.0241 0.0255 288.9513

120 0.0252 0.034 0.0423 53.4045 0.0307 -0.0132 0.0334 336.6619 0.0083 -0.0229 0.0244 289.9241

125 0.0284 0.0335 0.0439 49.6939 0.0293 -0.0117 0.0315 338.2894 0.0083 -0.0216 0.0232 290.9069

130 0.0309 0.0323 0.0447 46.2935 0.0275 -0.01 0.0292 340.052 0.0081 -0.0202 0.0218 291.8454

135 0.0322 0.03 0.044 42.994 0.0253 -0.0082 0.0266 342.0401 0.0078 -0.0186 0.0202 292.6313

140 0.0318 0.0262 0.0412 39.4461 0.0228 -0.0063 0.0237 344.4534 0.0072 -0.0169 0.0184 293.0285

145 0.0284 0.0197 0.0346 34.692 0.0202 -0.0044 0.0207 347.7343 0.0062 -0.0151 0.0163 292.4665

150 0.0194 0.0083 0.0211 23.2519 0.018 -0.0023 0.0181 352.7949 0.0046 -0.0131 0.0139 289.3484

155 -0.0026 -0.0136 0.0139 259.2961 0.0179 0.0002 0.0179 0.4963 0.0017 -0.0113 0.0115 278.4799

160 -0.0615 -0.0645 0.0891 226.3709 0.0271 0.0033 0.0273 6.8695 -0.0044 -0.0109 0.0117 248.0242

165 -0.3604 -0.299 0.4683 219.6852 0.1152 0.0103 0.1156 5.1072 -0.0259 -0.0251 0.0361 224.0765

170 -4.359 -3.0587 5.3251 215.0572 1.7621 0.0077 1.7621 0.2512 -0.2191 -0.3742 0.4336 239.6424

175 -3.5428 -2.0054 4.071 209.5122 2.0747 -0.0992 2.0771 357.2635 -0.0339 -0.5099 0.5111 266.2019

180 -0.4029 -0.1495 0.4297 200.3583 0.3652 -0.0272 0.3662 355.7458 0.0258 -0.1015 0.1047 284.2817

185 -0.1203 -0.0015 0.1203 180.7214 0.1839 -0.0161 0.1846 354.995 0.0256 -0.0552 0.0609 294.8396

190 -0.039 0.0372 0.0539 136.3837 0.1242 -0.0118 0.1247 354.5693 0.0245 -0.039 0.046 302.073

195 -0.0054 0.052 0.0522 95.934 0.0957 -0.0096 0.0961 354.2663 0.0236 -0.0307 0.0387 307.6069

200 0.0109 0.0587 0.0598 79.4653 0.0792 -0.0083 0.0796 353.9809 0.0231 -0.0254 0.0344 312.2705

205 0.0193 0.0621 0.065 72.7227 0.0684 -0.0076 0.0688 353.6643 0.0228 -0.0217 0.0315 316.4493

210 0.0235 0.0636 0.0678 69.7526 0.0608 -0.0071 0.0612 353.2956 0.0226 -0.0188 0.0294 320.3306

215 0.0313 0.0668 0.0738 64.9186 0.0487 -0.0061 0.049 352.9092 0.0212 -0.0148 0.0258 325.0552

220 0.0308 0.0665 0.0732 65.1599 0.0445 -0.0059 0.0449 352.3942 0.021 -0.0128 0.0246 328.5939

225 0.0294 0.0657 0.0719 65.8904 0.0409 -0.0059 0.0413 351.8018 0.0209 -0.0111 0.0237 331.9944

230 0.0275 0.0646 0.0702 66.9353 0.0376 -0.0059 0.038 351.1064 0.0207 -0.0095 0.0228 335.2763

235 0.0254 0.0634 0.0682 68.1823 0.0344 -0.0059 0.0349 350.2658 0.0204 -0.008 0.0219 338.4638

240 0.0231 0.062 0.0662 69.554 0.0312 -0.0059 0.0318 349.2153 0.0199 -0.0066 0.021 341.5929

245 0.0209 0.0607 0.0642 70.9954 0.0281 -0.006 0.0287 347.8589 0.0193 -0.0053 0.0201 344.7188

250 0.0188 0.0594 0.0623 72.4677 0.0248 -0.0062 0.0256 346.0539 0.0185 -0.004 0.019 347.9255

255 0.0167 0.0581 0.0605 73.9453 0.0215 -0.0063 0.0224 343.586 0.0175 -0.0027 0.0177 351.3416

260 0.0148 0.057 0.0589 75.4144 0.0182 -0.0066 0.0194 340.1282 0.0162 -0.0014 0.0163 355.169

265 0.0126 0.0557 0.0571 77.2983 0.0155 -0.0072 0.017 335.0597 0.0151 -0.0003 0.0151 358.7694

270 0.011 0.0547 0.0558 78.5928 0.0119 -0.0075 0.0141 327.8163 0.0131 0.0011 0.0132 4.6866

275 0.0094 0.0531 0.0539 79.9311 0.0084 -0.0078 0.0114 317.0421 0.0111 0.0028 0.0114 14.2039

280 0.0078 0.0514 0.052 81.3382 0.0051 -0.0082 0.0096 301.8373 0.0086 0.0043 0.0096 26.611

285 0.0062 0.0492 0.0496 82.8479 0.0019 -0.0085 0.0087 282.5841 0.0058 0.0059 0.0082 45.4163

290 0.0044 0.0461 0.0463 84.5315 -0.0012 -0.0088 0.0089 262.5608 0.0027 0.0075 0.008 70.2188

295 0.0025 0.0418 0.0418 86.5431 -0.0041 -0.0089 0.0098 245.286 -0.0006 0.0094 0.0094 93.748

300 0.0005 0.0357 0.0357 89.2661 -0.0069 -0.0087 0.0111 231.4541 -0.0042 0.0115 0.0122 110.1733

305 -0.0019 0.0272 0.0273 93.9005 -0.0096 -0.0081 0.0126 219.9446 -0.0081 0.0138 0.016 120.2958

310 -0.0045 0.0154 0.0161 106.4261 -0.0121 -0.0068 0.0139 209.4116 -0.0122 0.0166 0.0206 126.4014

315 -0.0079 -0.001 0.008 187.4328 -0.0142 -0.0048 0.015 198.6994 -0.0167 0.0199 0.026 130.0158

320 -0.0126 -0.0254 0.0284 243.692 -0.0157 -0.0015 0.0158 185.5491 -0.0216 0.0243 0.0325 131.6409

325 -0.0196 -0.0603 0.0634 252.0165 -0.015 0.0026 0.0152 170.0022 -0.0271 0.0296 0.0401 132.4775

330 -0.0321 -0.117 0.1213 254.6491 -0.0098 0.008 0.0127 140.7372 -0.0334 0.0367 0.0497 132.2776

335 -0.0713 -0.267 0.2763 255.0481 0.0181 0.0135 0.0226 36.653 -0.0432 0.0503 0.0664 130.6576

340 -0.1863 -0.6295 0.6564 253.5166 0.1132 0.0106 0.1137 5.3565 -0.0489 0.0668 0.0828 126.1846

345 -0.973 -2.7163 2.8853 250.2916 0.8208 -0.1084 0.8279 352.4797 0.017 0.0547 0.0573 72.7241

350 -48.4744 -103.0615 113.8923 244.8103 46.1432 -12.7338 47.868 344.5726 10.3799 -8.9013 13.6739 319.3854

355 -0.7866 -1.1897 1.4262 236.5282 0.7451 -0.2808 0.7962 339.3495 0.2535 -0.2736 0.373 312.8188

360 -0.2109 -0.1908 0.2844 222.1323 0.1678 -0.0703 0.1819 337.2586 0.0729 -0.0926 0.1179 308.2133

Appendix A18


theta2

degree

F32x

/10.^7

N

F32y

/10.^7

N

F32

/10.^7

N

theta32

degree

F43x

/10.^7

N

F43y

/10.^7

N

F43

/10.^7

N

theta43

degree

F53x

/10.^7

N

F53y

/10.^7

N

F53

/10.^7

N

theta53

degree

F65x

/10.^7

N

F65y

/10.^7

N

F65

/10.^7

N

theta65

degree

T/10.^3

N.m

0 0.1974 0.1908 0.2745 44.0315 0.1308 0.1832 0.2251 54.4648 -0.0398 -0.0749 0.0848 242.043 -0.0398 -0.0749 0.0848 242.043 -580.586

5 0.1169 0.0836 0.1437 35.5856 0.0733 0.098 0.1223 53.1959 -0.0251 -0.0562 0.0616 245.982 -0.0251 -0.0562 0.0616 245.982 -222.491

10 0.0887 0.0539 0.1038 31.2914 0.0515 0.0682 0.0854 52.9424 -0.0162 -0.042 0.045 248.952 -0.0162 -0.042 0.045 248.952 -114.678

15 0.0769 0.0444 0.0888 30.0416 0.0418 0.0547 0.0688 52.6112 -0.0101 -0.0321 0.0337 252.549 -0.0101 -0.0321 0.0337 252.549 -70.1159

20 0.0708 0.0397 0.0812 29.3003 0.0374 0.0468 0.0599 51.308 -0.0065 -0.0266 0.0273 256.251 -0.0065 -0.0266 0.0273 256.251 -39.9349

25 0.0669 0.0358 0.0759 28.1313 0.0357 0.0411 0.0545 49.0317 -0.0047 -0.0242 0.0246 259.01 -0.0047 -0.0242 0.0246 259.01 -12.6144

30 0.0635 0.0311 0.0707 26.1035 0.0353 0.0365 0.0507 45.9773 -0.0044 -0.0244 0.0248 259.742 -0.0044 -0.0244 0.0248 259.742 14.6262

35 0.0599 0.0254 0.065 23.0321 0.0355 0.0324 0.0481 42.4164 -0.0054 -0.0267 0.0273 258.499 -0.0054 -0.0267 0.0273 258.499 41.043

40 0.0554 0.0185 0.0584 18.4258 0.0361 0.0287 0.0461 38.5034 -0.0078 -0.031 0.0319 255.874 -0.0078 -0.031 0.0319 255.874 65.3766

45 0.0507 0.0114 0.052 12.6287 0.0369 0.0255 0.0449 34.7101 -0.0107 -0.036 0.0376 253.379 -0.0107 -0.036 0.0376 253.379 84.6515

50 0.0455 0.004 0.0457 5.03 0.0378 0.0228 0.0441 31.1141 -0.0143 -0.0417 0.0441 251.069 -0.0143 -0.0417 0.0441 251.069 98.2707

55 0.04 -0.0033 0.0402 355.29 0.0388 0.0205 0.0439 27.8455 -0.0183 -0.0478 0.0512 249.083 -0.0183 -0.0478 0.0512 249.083 105.534

60 0.0344 -0.0103 0.0359 343.295 0.0398 0.0185 0.0439 24.9721 -0.0224 -0.0539 0.0584 247.425 -0.0224 -0.0539 0.0584 247.425 106.295

65 0.0287 -0.0169 0.0333 329.541 0.0408 0.0169 0.0442 22.5099 -0.0265 -0.0597 0.0653 246.053 -0.0265 -0.0597 0.0653 246.053 100.858

70 0.0231 -0.0229 0.0325 315.299 0.0418 0.0156 0.0446 20.4398 -0.0305 -0.0651 0.0718 244.922 -0.0305 -0.0651 0.0718 244.922 89.8576

75 0.0177 -0.0282 0.0333 302.071 0.0426 0.0144 0.045 18.7239 -0.0341 -0.0699 0.0777 243.987 -0.0341 -0.0699 0.0777 243.987 74.1452

80 0.013 -0.0317 0.0343 292.293 0.0431 0.0137 0.0452 17.6185 -0.0365 -0.073 0.0816 243.444 -0.0365 -0.073 0.0816 243.444 55.7414

85 0.0081 -0.0356 0.0365 282.815 0.0435 0.013 0.0454 16.6141 -0.0392 -0.0764 0.0858 242.83 -0.0392 -0.0764 0.0858 242.83 33.99

90 0.0035 -0.0388 0.039 275.079 0.0438 0.0124 0.0455 15.8464 -0.0414 -0.0791 0.0893 242.335 -0.0414 -0.0791 0.0893 242.335 10.5035

95 -0.0009 -0.0414 0.0415 268.731 0.0437 0.0119 0.0453 15.2746 -0.0432 -0.081 0.0918 241.941 -0.0432 -0.081 0.0918 241.941 -13.7758

100 -0.005 -0.0435 0.0437 263.433 0.0434 0.0115 0.0449 14.8651 -0.0444 -0.0822 0.0935 241.637 -0.0444 -0.0822 0.0935 241.637 -37.9497

105 -0.0088 -0.0449 0.0457 258.919 0.0428 0.0112 0.0443 14.5918 -0.0451 -0.0827 0.0942 241.415 -0.0451 -0.0827 0.0942 241.415 -61.1664

110 -0.0123 -0.0457 0.0473 254.992 0.0419 0.0108 0.0433 14.4356 -0.0452 -0.0824 0.094 241.271 -0.0452 -0.0824 0.094 241.271 -82.6129

115 -0.0157 -0.0461 0.0487 251.176 0.0409 0.0101 0.0422 13.9318 -0.0453 -0.0812 0.093 240.868 -0.0453 -0.0812 0.093 240.868 -102.641

120 -0.0184 -0.0457 0.0493 248.027 0.0395 0.0098 0.0407 13.8727 -0.0443 -0.0793 0.0908 240.794 -0.0443 -0.0793 0.0908 240.794 -118.167

125 -0.0206 -0.0446 0.0492 245.168 0.0379 0.0094 0.039 13.903 -0.0428 -0.0765 0.0876 240.785 -0.0428 -0.0765 0.0876 240.785 -129.352

130 -0.0221 -0.0427 0.0481 242.577 0.0361 0.009 0.0372 14.0507 -0.0406 -0.0727 0.0833 240.853 -0.0406 -0.0727 0.0833 240.853 -135.079

135 -0.0226 -0.0396 0.0456 240.289 0.0343 0.0088 0.0354 14.3816 -0.0375 -0.0678 0.0775 241.028 -0.0375 -0.0678 0.0775 241.028 -133.812

140 -0.0214 -0.0349 0.0409 238.466 0.0328 0.0088 0.034 15.0294 -0.0335 -0.0613 0.0699 241.385 -0.0335 -0.0613 0.0699 241.385 -123.129

145 -0.0173 -0.0275 0.0325 237.757 0.032 0.0093 0.0333 16.2409 -0.0279 -0.0527 0.0596 242.134 -0.0279 -0.0527 0.0596 242.134 -98.6727

150 -0.0076 -0.0151 0.0169 243.211 0.0329 0.0109 0.0347 18.3926 -0.0196 -0.0403 0.0449 244.07 -0.0196 -0.0403 0.0449 244.07 -51.4048

155 0.0149 0.0079 0.0168 28.0048 0.0383 0.0153 0.0412 21.7839 -0.006 -0.0207 0.0215 253.779 -0.006 -0.0207 0.0215 253.779 40.9292

160 0.0742 0.0599 0.0954 38.8863 0.0569 0.0277 0.0633 25.9333 0.0215 0.0175 0.0278 39.1346 0.0215 0.0175 0.0278 39.1346 248.487

165 0.3735 0.2955 0.4763 38.3538 0.1636 0.0972 0.1903 30.7205 0.132 0.162 0.209 50.8178 0.132 0.162 0.209 50.8178 1162.8

170 4.3724 3.0564 5.3347 34.9541 1.6745 1.011 1.956 31.1238 1.3296 1.6265 2.1008 50.7365 1.3296 1.6265 2.1008 50.7365 11470

175 3.5563 2.0043 4.0822 29.4044 1.4336 0.8039 1.6436 29.2821 0.7426 0.7551 1.0591 45.4797 0.7426 0.7551 1.0591 45.4797 7018.9

180 0.4164 0.1495 0.4425 19.7474 0.1981 0.0967 0.2205 26.024 0.0258 -0.0207 0.0331 321.264 0.0258 -0.0207 0.0331 321.264 454.923

185 0.1338 0.0027 0.1338 1.1547 0.0819 0.0327 0.0882 21.7608 -0.023 -0.0639 0.068 250.226 -0.023 -0.0639 0.068 250.226 -27.3034

190 0.0524 -0.0348 0.0629 326.38 0.0466 0.0137 0.0486 16.3258 -0.0327 -0.0686 0.076 244.472 -0.0327 -0.0686 0.076 244.472 -132.029

195 0.0185 -0.0485 0.0519 290.896 0.0308 0.0052 0.0313 9.5948 -0.0347 -0.0664 0.0749 242.407 -0.0347 -0.0664 0.0749 242.407 -157.008

200 0.0018 -0.0541 0.0541 271.924 0.0223 0.0007 0.0223 1.6858 -0.0344 -0.0626 0.0714 241.226 -0.0344 -0.0626 0.0714 241.226 -156.623

205 -0.007 -0.0563 0.0568 262.901 0.0173 -0.002 0.0174 353.249 -0.0333 -0.0585 0.0673 240.349 -0.0333 -0.0585 0.0673 240.349 -146.377

210 -0.0117 -0.0569 0.0581 258.343 0.0141 -0.0037 0.0146 345.294 -0.0319 -0.0544 0.0631 239.58 -0.0319 -0.0544 0.0631 239.58 -131.992

215 -0.0202 -0.0591 0.0624 251.141 0.0079 -0.0073 0.0107 317.082 -0.0297 -0.0488 0.0571 238.715 -0.0297 -0.0488 0.0571 238.715 -111.996

220 -0.0204 -0.0577 0.0612 250.563 0.0067 -0.0078 0.0103 310.734 -0.0281 -0.0449 0.053 237.955 -0.0281 -0.0449 0.053 237.955 -94.7473

225 -0.0198 -0.0561 0.0595 250.554 0.0059 -0.008 0.0099 306.364 -0.0266 -0.0411 0.049 237.136 -0.0266 -0.0411 0.049 237.136 -78.0701

230 -0.0188 -0.0542 0.0574 250.883 0.0052 -0.0081 0.0096 302.831 -0.0251 -0.0375 0.0451 236.232 -0.0251 -0.0375 0.0451 236.232 -62.2387

235 -0.0176 -0.0522 0.0551 251.398 0.0045 -0.008 0.0092 299.049 -0.0236 -0.034 0.0414 235.219 -0.0236 -0.034 0.0414 235.219 -47.3593

240 -0.0163 -0.0503 0.0529 251.994 0.0036 -0.0081 0.0088 294.032 -0.0221 -0.0305 0.0377 234.064 -0.0221 -0.0305 0.0377 234.064 -33.4333

245 -0.0152 -0.0484 0.0507 252.596 0.0025 -0.0083 0.0086 287.025 -0.0206 -0.0271 0.0341 232.72 -0.0206 -0.0271 0.0341 232.72 -20.398

250 -0.0141 -0.0466 0.0487 253.154 0.0012 -0.0086 0.0087 277.866 -0.0191 -0.0237 0.0305 231.114 -0.0191 -0.0237 0.0305 231.114 -8.1578

255 -0.0132 -0.045 0.0469 253.641 -0.0004 -0.0093 0.0093 267.411 -0.0176 -0.0203 0.0268 229.125 -0.0176 -0.0203 0.0268 229.125 3.3883

260 -0.0125 -0.0436 0.0454 254.045 -0.0023 -0.0103 0.0105 257.279 -0.0159 -0.0168 0.0231 226.538 -0.0159 -0.0168 0.0231 226.538 14.3201

265 -0.0114 -0.0422 0.0437 254.917 -0.0039 -0.0112 0.0119 250.603 -0.0145 -0.0137 0.02 223.477 -0.0145 -0.0137 0.02 223.477 23.3047

270 -0.011 -0.0411 0.0426 254.983 -0.0066 -0.013 0.0145 243.166 -0.0125 -0.0098 0.0159 218.097 -0.0125 -0.0098 0.0159 218.097 33.5842

275 -0.0106 -0.0396 0.041 254.994 -0.0095 -0.0149 0.0176 237.514 -0.0103 -0.0054 0.0116 207.842 -0.0103 -0.0054 0.0116 207.842 42.6519

280 -0.0102 -0.0381 0.0394 255.02 -0.0124 -0.017 0.0211 233.804 -0.008 -0.001 0.0081 187.409 -0.008 -0.001 0.0081 187.409 50.6731

285 -0.0097 -0.0361 0.0374 254.989 -0.0155 -0.0191 0.0246 230.89 -0.0056 0.0037 0.0067 146.596 -0.0056 0.0037 0.0067 146.596 56.9197

290 -0.0091 -0.0334 0.0346 254.822 -0.0188 -0.0211 0.0283 228.315 -0.0029 0.0089 0.0094 108.241 -0.0029 0.0089 0.0094 108.241 60.6188

295 -0.0083 -0.0295 0.0306 254.353 -0.0222 -0.0228 0.0318 225.712 0 0.0147 0.0147 89.9063 0 0.0147 0.0147 89.9063 60.6601

300 -0.0072 -0.0239 0.025 253.169 -0.0258 -0.0238 0.0351 222.75 0.0034 0.0214 0.0217 81.095 0.0034 0.0214 0.0217 81.095 55.4753

305 -0.0059 -0.0161 0.0171 249.786 -0.0296 -0.024 0.0381 219.071 0.0071 0.0291 0.03 76.2063 0.0071 0.0291 0.03 76.2063 42.8478

310 -0.0042 -0.005 0.0065 230.402 -0.0336 -0.0228 0.0406 214.226 0.0116 0.0383 0.0401 73.2022 0.0116 0.0383 0.0401 73.2022 19.5745

315 -0.0017 0.0106 0.0108 99.0556 -0.0379 -0.0198 0.0427 207.556 0.0169 0.0497 0.0525 71.2418 0.0169 0.0497 0.0525 71.2418 -19.2082

320 0.0022 0.0341 0.0342 86.3446 -0.0427 -0.0135 0.0448 197.58 0.0239 0.065 0.0693 69.827 0.0239 0.065 0.0693 69.827 -83.8504

325 0.0085 0.0681 0.0686 82.9106 -0.0475 -0.0029 0.0476 183.476 0.0326 0.0849 0.091 68.9985 0.0326 0.0849 0.091 68.9985 -184.504

330 0.0204 0.1238 0.1254 80.6526 -0.0522 0.0167 0.0548 162.274 0.0452 0.1149 0.1235 68.5043 0.0452 0.1149 0.1235 68.5043 -357.199

335 0.059 0.2727 0.279 77.7914 -0.0551 0.0739 0.0922 126.689 0.074 0.1873 0.2014 68.4549 0.074 0.1873 0.2014 68.4549 -827.907

340 0.1735 0.6341 0.6574 74.6964 -0.0377 0.2289 0.232 99.3527 0.1308 0.3376 0.362 68.8214 0.1308 0.3376 0.362 68.8214 -1993.8

345 0.9599 2.7198 2.8842 70.5601 0.2059 1.2232 1.2405 80.4443 0.379 1.0429 1.1097 70.0306 0.379 1.0429 1.1097 70.0306 -8750.4

350 48.4611 103.064 113.89 64.8169 22.9485 57.1513 61.5866 68.1226 6.1604 21.9529 22.8009 74.3249 6.1604 21.9529 22.8009 74.3249 -334470

355 0.7731 1.1908 1.4198 57.0093 0.4744 0.8265 0.9529 60.1454 -0.0507 -0.0072 0.0512 188.105 -0.0507 -0.0072 0.0512 188.105 -3815

360 0.1974 0.1908 0.2745 44.0315 0.1308 0.1832 0.2251 54.4648 -0.0398 -0.0749 0.0848 242.043 -0.0398 -0.0749 0.0848 242.043 -580.586

Appendix A19


theta2

degree

F12x

/10.^7

N

F12y

/10.^7

N

F12

/10.^7

N

theta12

degree

F14x

/10.^7

N

F14y

/10.^7

N

F14

/10.^7

N

theta14

degree

F16x

/10.^7

N

F16y

/10.^7

N

F16

/10.^7

N

theta16

degree

0 -0.2066 -0.1883 0.2795 222.3374 0.164 -0.0683 0.1777 337.4001 0.0723 -0.0974 0.1213 306.6032

5 -0.1276 -0.082 0.1517 212.7133 0.0801 -0.0309 0.0859 338.9255 0.0382 -0.0588 0.0701 303.0118

10 -0.0998 -0.0535 0.1132 208.1792 0.0494 -0.0147 0.0515 343.4868 0.023 -0.0411 0.0471 299.2399

15 -0.0879 -0.0452 0.0989 207.2067 0.0356 -0.0063 0.0362 349.9492 0.0152 -0.0312 0.0347 296.0161

20 -0.0816 -0.0417 0.0916 207.0406 0.0289 -0.0026 0.029 354.9552 0.0107 -0.0257 0.0279 292.5065

25 -0.0773 -0.0389 0.0865 206.6809 0.0256 -0.0016 0.0256 356.5192 0.008 -0.0227 0.0241 289.3805

30 -0.0734 -0.0353 0.0815 205.7101 0.024 -0.0023 0.0241 354.4735 0.0065 -0.0214 0.0223 286.8482

35 -0.0692 -0.0308 0.0757 204.0071 0.0233 -0.0041 0.0237 349.9443 0.0056 -0.0211 0.0218 284.9848

40 -0.0641 -0.0249 0.0688 201.2552 0.0233 -0.0066 0.0242 344.1486 0.005 -0.0219 0.0224 282.9012

45 -0.0587 -0.0189 0.0616 197.8464 0.0236 -0.0091 0.0253 338.8327 0.0049 -0.0228 0.0233 282.1453

50 -0.0527 -0.0125 0.0542 193.373 0.0242 -0.0116 0.0268 334.3897 0.005 -0.0239 0.0244 281.7387

55 -0.0464 -0.0062 0.0468 187.5492 0.025 -0.0138 0.0285 331.0373 0.0051 -0.0251 0.0256 281.5816

60 -0.0399 0 0.0399 179.9464 0.0259 -0.0158 0.0304 328.7231 0.0054 -0.0262 0.0267 281.6108

65 -0.0333 0.0059 0.0338 170.0053 0.027 -0.0174 0.0321 327.287 0.0057 -0.0271 0.0277 281.7882

70 -0.0267 0.0112 0.029 157.2137 0.0282 -0.0186 0.0338 326.5514 0.006 -0.0278 0.0284 282.0905

75 -0.0203 0.0161 0.0259 141.6476 0.0293 -0.0195 0.0352 326.3588 0.0063 -0.0282 0.0289 282.5032

80 -0.0146 0.0192 0.0241 127.2447 0.0299 -0.0195 0.0357 326.8933 0.0065 -0.0284 0.0291 282.968

85 -0.0086 0.0228 0.0244 110.7323 0.0308 -0.0196 0.0365 327.5397 0.0069 -0.0284 0.0292 283.5887

90 -0.0029 0.0259 0.026 96.4229 0.0315 -0.0194 0.037 328.4414 0.0072 -0.0282 0.0291 284.3003

95 0.0025 0.0284 0.0286 84.9143 0.0321 -0.0189 0.0372 329.538 0.0075 -0.0279 0.0289 285.0978

100 0.0077 0.0305 0.0315 75.8738 0.0324 -0.0181 0.0371 330.7851 0.0078 -0.0273 0.0284 285.9772

105 0.0125 0.0321 0.0345 68.7177 0.0324 -0.0171 0.0367 332.151 0.0081 -0.0266 0.0278 286.9348

110 0.017 0.0333 0.0374 62.9312 0.0322 -0.016 0.0359 333.6153 0.0083 -0.0257 0.0271 287.966

115 0.0214 0.0341 0.0402 57.8172 0.0317 -0.0149 0.0351 334.8528 0.0082 -0.0243 0.0257 288.7119

120 0.0251 0.0342 0.0424 53.7237 0.0308 -0.0134 0.0336 336.4219 0.0083 -0.0231 0.0246 289.7666

125 0.0281 0.0337 0.0439 50.1246 0.0295 -0.0119 0.0318 338.0805 0.0083 -0.0218 0.0233 290.8241

130 0.0304 0.0325 0.0445 46.8456 0.0279 -0.0102 0.0297 339.8663 0.0081 -0.0203 0.0219 291.8267

135 0.0316 0.0302 0.0437 43.6935 0.0259 -0.0085 0.0272 341.8622 0.0078 -0.0187 0.0203 292.6579

140 0.031 0.0263 0.0407 40.3455 0.0236 -0.0066 0.0245 344.244 0.0072 -0.017 0.0185 293.0636

145 0.0275 0.0199 0.0339 35.9071 0.0211 -0.0047 0.0217 347.3881 0.0062 -0.0151 0.0164 292.4303

150 0.0184 0.0086 0.0203 25.1351 0.019 -0.0026 0.0192 352.0621 0.0046 -0.0133 0.014 289.059

155 -0.0031 -0.0131 0.0135 256.6611 0.0186 -0.0003 0.0186 359.1989 0.0016 -0.0116 0.0117 277.638

160 -0.0595 -0.0635 0.087 226.8294 0.0254 0.0028 0.0256 6.3492 -0.0047 -0.0117 0.0126 248.0868

165 -0.3397 -0.2949 0.4499 220.9648 0.0952 0.0099 0.0958 5.9498 -0.0267 -0.0291 0.0394 227.4475

170 -3.9951 -3.0093 5.0017 216.989 1.397 0.0101 1.3971 0.4129 -0.218 -0.4261 0.4786 242.9048

175 -3.1154 -1.9574 3.6793 212.1414 1.635 -0.0969 1.6379 356.6089 -0.0216 -0.5604 0.5609 267.7971

180 -0.3301 -0.142 0.3593 203.2718 0.2888 -0.0275 0.2901 354.5646 0.0294 -0.1089 0.1128 285.0941

185 -0.085 0.002 0.085 178.6253 0.1462 -0.0167 0.1472 353.4806 0.0279 -0.0584 0.0647 295.5343

190 -0.0162 0.0395 0.0427 112.2788 0.0995 -0.0125 0.1003 352.828 0.0263 -0.0408 0.0486 302.7898

195 0.0113 0.0537 0.0549 78.087 0.0773 -0.0104 0.078 352.3732 0.0252 -0.0319 0.0406 308.3772

200 0.0239 0.0601 0.0647 68.2765 0.0647 -0.0091 0.0654 352.0018 0.0246 -0.0262 0.0359 313.0877

205 0.0298 0.0632 0.0698 64.7734 0.0567 -0.0083 0.0573 351.6625 0.0241 -0.0223 0.0328 317.2972

210 0.032 0.0645 0.072 63.6282 0.0511 -0.0078 0.0517 351.3306 0.0238 -0.0192 0.0306 321.1916

215 0.0378 0.0674 0.0773 60.7265 0.0411 -0.0066 0.0416 350.8111 0.0222 -0.015 0.0268 325.9818

220 0.0361 0.0669 0.076 61.6426 0.0382 -0.0064 0.0387 350.4333 0.022 -0.013 0.0255 329.5073

225 0.0337 0.0659 0.074 62.9051 0.0357 -0.0063 0.0362 350.0141 0.0218 -0.0111 0.0244 332.884

230 0.031 0.0647 0.0717 64.3931 0.0333 -0.0062 0.0339 349.5131 0.0215 -0.0095 0.0235 336.1364

235 0.0281 0.0633 0.0692 66.0227 0.0309 -0.0061 0.0315 348.8753 0.0211 -0.008 0.0225 339.2933

240 0.0253 0.0618 0.0668 67.7314 0.0284 -0.006 0.0291 348.0267 0.0206 -0.0065 0.0216 342.395

245 0.0226 0.0603 0.0644 69.4711 0.0258 -0.006 0.0265 346.8652 0.0199 -0.0051 0.0206 345.5011

250 0.02 0.0589 0.0622 71.2054 0.0231 -0.0061 0.0238 345.2449 0.019 -0.0038 0.0194 348.6998

255 0.0177 0.0576 0.0602 72.909 0.0201 -0.0062 0.0211 342.9505 0.0179 -0.0025 0.0181 352.1239

260 0.0155 0.0563 0.0584 74.5668 0.0171 -0.0064 0.0183 339.6536 0.0166 -0.0012 0.0166 355.9802

265 0.0131 0.055 0.0566 76.5929 0.0146 -0.0069 0.0162 334.7218 0.0154 -0.0001 0.0154 359.609

270 0.0115 0.0539 0.0551 78.0043 0.0113 -0.0072 0.0133 327.5554 0.0134 0.0013 0.0135 5.6172

275 0.0098 0.0522 0.0531 79.4145 0.0078 -0.0074 0.0108 316.6817 0.0113 0.0031 0.0117 15.1909

280 0.0081 0.0505 0.0511 80.858 0.0046 -0.0077 0.009 300.949 0.0088 0.0046 0.0099 27.6245

285 0.0065 0.0481 0.0486 82.3653 0.0015 -0.008 0.0081 280.4885 0.0059 0.0062 0.0086 46.1413

290 0.0047 0.0449 0.0451 84.0075 -0.0016 -0.0081 0.0083 258.9531 0.0029 0.0079 0.0084 70.1198

295 0.0029 0.0404 0.0405 85.936 -0.0046 -0.0081 0.0093 240.5093 -0.0005 0.0098 0.0098 92.8543

300 0.0009 0.0341 0.0341 88.5325 -0.0075 -0.0077 0.0107 225.8998 -0.0041 0.0119 0.0126 108.9889

305 -0.0013 0.0253 0.0254 93.0467 -0.0103 -0.0069 0.0124 213.7764 -0.0079 0.0143 0.0163 119.1056

310 -0.0039 0.0133 0.0138 106.5332 -0.0129 -0.0054 0.0139 202.6395 -0.0121 0.0171 0.0209 125.2877

315 -0.0072 -0.0036 0.008 206.6308 -0.0151 -0.003 0.0154 191.2664 -0.0166 0.0205 0.0263 128.9905

320 -0.0117 -0.0285 0.0308 247.7034 -0.0168 0.0007 0.0168 177.5582 -0.0214 0.0249 0.0329 130.6998

325 -0.0185 -0.064 0.0666 253.8951 -0.0163 0.0055 0.0172 161.3988 -0.0268 0.0302 0.0404 131.607

330 -0.0307 -0.1217 0.1255 255.8339 -0.0116 0.0119 0.0166 134.3282 -0.0331 0.0374 0.0499 131.4698

335 -0.069 -0.2743 0.2829 255.8798 0.0152 0.0201 0.0252 52.9654 -0.0426 0.0509 0.0664 129.9141

340 -0.1815 -0.6424 0.6676 254.2207 0.1071 0.0236 0.1097 12.4396 -0.0475 0.0666 0.0818 125.5055

345 -0.952 -2.7573 2.9171 250.9519 0.7943 -0.0588 0.7965 355.7686 0.0225 0.0459 0.0511 63.9579

350 -47.5087 -104.0869 114.4166 245.4665 45.0164 -10.9896 46.3384 346.2811 10.541 -9.6203 14.271 317.6146

355 -0.7711 -1.194 1.4213 237.1426 0.729 -0.2617 0.7746 340.2497 0.2542 -0.2886 0.3846 311.3732

360 -0.2066 -0.1883 0.2795 222.3374 0.164 -0.0683 0.1777 337.4001 0.0723 -0.0974 0.1213 306.6032

Appendix A19


theta2

degree

F32x

/10.^7

N

F32y

/10.^7

N

F32

/10.^7

N

theta32

degree

F43x

/10.^7

N

F43y

/10.^7

N

F43

/10.^7

N

theta43

degree

F53x

/10.^7

N

F53y

/10.^7

N

F53

/10.^7

N

theta53

degree

F65x

/10.^7

N

F65y

/10.^7

N

F65

/10.^7

N

theta65

degree

T/10.^3

N.m

0 0.1931 0.1882 0.2696 44.2728 0.1271 0.1853 0.2247 55.5476 -0.0403 -0.0797 0.0893 243.141 0.09 0.011 0.0907 6.9812 -572.838

5 0.1141 0.0808 0.1398 35.2859 0.0712 0.0981 0.1213 54.0294 -0.0257 -0.0593 0.0647 246.556 0.0546 0.005 0.0548 5.2826 -214.637

10 0.0865 0.0511 0.1004 30.575 0.05 0.0677 0.0841 53.5677 -0.0169 -0.0444 0.0475 249.19 0.0394 0.0049 0.0397 7.023 -107.488

15 0.0748 0.0417 0.0856 29.1029 0.0405 0.0539 0.0674 53.0723 -0.0109 -0.0342 0.0359 252.405 0.032 0.006 0.0326 10.6151 -63.5962

20 0.0689 0.037 0.0782 28.2344 0.0363 0.0458 0.0585 51.6328 -0.0073 -0.0285 0.0294 255.664 0.0281 0.0066 0.0288 13.1887 -34.1612

25 0.065 0.0331 0.073 26.9669 0.0346 0.0401 0.053 49.2337 -0.0055 -0.026 0.0265 258.063 0.026 0.0066 0.0268 14.1549 -7.7061

30 0.0617 0.0285 0.0679 24.8261 0.0342 0.0355 0.0493 46.0631 -0.0052 -0.0261 0.0266 258.692 0.025 0.0059 0.0257 13.2328 18.5637

35 0.0581 0.023 0.0625 21.6025 0.0345 0.0315 0.0467 42.3946 -0.0062 -0.0283 0.029 257.584 0.0245 0.0046 0.025 10.5921 43.9562

40 0.0537 0.0162 0.0561 16.7641 0.0351 0.0278 0.0448 38.3858 -0.0086 -0.0325 0.0336 255.206 0.0242 0.0025 0.0243 5.9338 67.2769

45 0.0491 0.0093 0.0499 10.6871 0.036 0.0248 0.0437 34.5225 -0.0115 -0.0374 0.0391 252.908 0.0241 0.0004 0.0241 1.0353 85.6098

50 0.044 0.0021 0.0441 2.7434 0.037 0.0221 0.0431 30.8822 -0.015 -0.043 0.0456 250.747 0.0242 -0.0018 0.0242 355.749 98.4021

55 0.0386 -0.005 0.039 352.635 0.0381 0.0199 0.0429 27.5937 -0.0189 -0.049 0.0525 248.864 0.0242 -0.004 0.0245 350.503 104.979

60 0.0331 -0.0118 0.0352 340.358 0.0392 0.018 0.0431 24.7199 -0.023 -0.0549 0.0596 247.276 0.0241 -0.0062 0.0249 345.618 105.205

65 0.0276 -0.0182 0.033 326.571 0.0402 0.0165 0.0435 22.2705 -0.0271 -0.0606 0.0664 245.954 0.0241 -0.0082 0.0254 341.28 99.3816

70 0.0221 -0.024 0.0326 312.619 0.0412 0.0152 0.0439 20.2204 -0.0309 -0.0659 0.0728 244.857 0.0239 -0.0099 0.0259 337.563 88.1325

75 0.0168 -0.0292 0.0337 299.894 0.0421 0.0141 0.0444 18.5267 -0.0345 -0.0706 0.0786 243.948 0.0238 -0.0114 0.0264 334.458 72.2939

80 0.0122 -0.0326 0.0348 290.587 0.0427 0.0134 0.0447 17.4336 -0.0368 -0.0736 0.0823 243.421 0.0235 -0.0125 0.0266 331.892 53.8913

85 0.0074 -0.0363 0.0371 281.581 0.0432 0.0127 0.045 16.4465 -0.0395 -0.0769 0.0865 242.823 0.0233 -0.0136 0.0269 329.739 32.2096

90 0.0029 -0.0395 0.0396 274.22 0.0435 0.0122 0.0451 15.6911 -0.0417 -0.0795 0.0898 242.34 0.023 -0.0144 0.0271 328 8.8637

95 -0.0013 -0.042 0.042 268.159 0.0435 0.0118 0.0451 15.1254 -0.0434 -0.0814 0.0923 241.956 0.0227 -0.015 0.0272 326.609 -15.2184

100 -0.0053 -0.0439 0.0442 263.084 0.0433 0.0114 0.0447 14.7147 -0.0445 -0.0826 0.0938 241.661 0.0224 -0.0154 0.0272 325.507 -39.151

105 -0.009 -0.0453 0.0462 258.749 0.0427 0.011 0.0441 14.4313 -0.0452 -0.083 0.0945 241.447 0.0221 -0.0157 0.0271 324.646 -62.0926

110 -0.0124 -0.046 0.0477 254.973 0.0419 0.0106 0.0432 14.2543 -0.0452 -0.0827 0.0942 241.309 0.0216 -0.0157 0.0268 323.992 -83.2389

115 -0.0157 -0.0464 0.049 251.297 0.041 0.01 0.0422 13.7155 -0.0453 -0.0814 0.0932 240.911 0.0208 -0.0153 0.0258 323.74 -102.937

120 -0.0183 -0.046 0.0495 248.283 0.0396 0.0096 0.0408 13.6073 -0.0443 -0.0794 0.091 240.842 0.0202 -0.0149 0.0251 323.521 -118.135

125 -0.0204 -0.0448 0.0493 245.568 0.0381 0.0092 0.0392 13.568 -0.0428 -0.0766 0.0877 240.835 0.0195 -0.0144 0.0242 323.533 -128.991

130 -0.0217 -0.0429 0.0481 243.148 0.0365 0.0088 0.0375 13.6201 -0.0405 -0.0728 0.0833 240.904 0.0187 -0.0136 0.0231 323.872 -134.406

135 -0.022 -0.0398 0.0455 241.08 0.0349 0.0086 0.0359 13.8233 -0.0375 -0.0678 0.0775 241.077 0.0177 -0.0125 0.0217 324.751 -132.866

140 -0.0206 -0.0351 0.0407 239.573 0.0335 0.0086 0.0346 14.3092 -0.0334 -0.0614 0.0699 241.427 0.0168 -0.011 0.0201 326.666 -121.999

145 -0.0164 -0.0277 0.0322 239.436 0.0329 0.009 0.0341 15.34 -0.0278 -0.0527 0.0596 242.164 0.0158 -0.0088 0.0181 330.85 -97.5454

150 -0.0066 -0.0154 0.0168 246.762 0.034 0.0106 0.0356 17.3718 -0.0196 -0.0404 0.0449 244.075 0.015 -0.0053 0.0159 340.687 -50.6904

155 0.0154 0.0074 0.0171 25.5709 0.0389 0.0149 0.0417 20.9785 -0.0061 -0.0209 0.0218 253.62 0.0151 0.0012 0.0152 4.3877 40.2291

160 0.0723 0.0588 0.0932 39.123 0.0553 0.0273 0.0616 26.2843 0.0212 0.0168 0.027 38.2903 0.0191 0.0156 0.0246 39.1782 243.405

165 0.3528 0.2914 0.4576 39.554 0.1436 0.0969 0.1733 34.001 0.1313 0.1581 0.2055 50.2924 0.0551 0.0794 0.0966 55.2286 1134.4

170 4.0084 3.0069 5.0109 36.8753 1.3094 1.0134 1.6558 37.7393 1.3307 1.5746 2.0616 49.7992 0.7139 0.8701 1.1255 50.6327 11129

175 3.1289 1.9562 3.6901 32.0138 0.9938 0.8062 1.2797 39.0495 0.7549 0.7047 1.0327 43.0304 0.8213 0.634 1.0375 37.6672 6760

180 0.3436 0.1419 0.3718 22.4408 0.1218 0.0965 0.1554 38.3855 0.0294 -0.0281 0.0406 316.275 0.1483 0.0625 0.1609 22.8396 431.966

185 0.0985 -0.0009 0.0985 359.48 0.0443 0.0321 0.0547 35.9536 -0.0207 -0.067 0.0702 252.866 0.0773 0.0148 0.0787 10.8371 -28.7362

190 0.0295 -0.0372 0.0475 308.467 0.0219 0.013 0.0255 30.6373 -0.0309 -0.0703 0.0768 246.28 0.0536 0.002 0.0536 2.1318 -126.92

195 0.0018 -0.0502 0.0502 272.021 0.0125 0.0045 0.0133 19.8391 -0.0331 -0.0675 0.0752 243.881 0.042 -0.0029 0.0421 356.075 -148.913

200 -0.0112 -0.0555 0.0566 258.589 0.0079 0 0.0079 359.724 -0.033 -0.0634 0.0714 242.523 0.0349 -0.005 0.0353 351.776 -146.954

205 -0.0175 -0.0575 0.0601 253.096 0.0055 -0.0027 0.0062 333.976 -0.032 -0.059 0.0671 241.531 0.03 -0.0061 0.0306 348.592 -135.919

210 -0.0202 -0.0577 0.0612 250.697 0.0044 -0.0043 0.0062 315.88 -0.0307 -0.0547 0.0628 240.676 0.0263 -0.0065 0.0271 346.096 -121.288

215 -0.0267 -0.0597 0.0654 245.908 0.0003 -0.0079 0.0079 272.221 -0.0286 -0.049 0.0567 239.698 0.021 -0.0072 0.0222 341.067 -102.117

220 -0.0257 -0.0582 0.0636 246.169 0.0004 -0.0083 0.0083 273.049 -0.0271 -0.045 0.0525 238.875 0.0185 -0.0071 0.0198 339.082 -85.2887

225 -0.0241 -0.0563 0.0613 246.822 0.0007 -0.0084 0.0084 274.809 -0.0257 -0.0411 0.0485 237.991 0.0163 -0.0069 0.0177 337.114 -69.2611

230 -0.0223 -0.0543 0.0587 247.701 0.0009 -0.0083 0.0083 276.394 -0.0243 -0.0374 0.0446 237.019 0.0143 -0.0067 0.0158 334.986 -54.2467

235 -0.0204 -0.0522 0.056 248.691 0.001 -0.0082 0.0082 276.919 -0.0229 -0.0339 0.0409 235.931 0.0123 -0.0064 0.0139 332.492 -40.2922

240 -0.0185 -0.0501 0.0534 249.705 0.0008 -0.0081 0.0081 275.628 -0.0215 -0.0304 0.0372 234.696 0.0104 -0.0062 0.0121 329.352 -27.3433

245 -0.0169 -0.0481 0.0509 250.675 0.0003 -0.0082 0.0082 272.019 -0.0201 -0.0269 0.0336 233.264 0.0085 -0.0059 0.0103 325.149 -15.2883

250 -0.0154 -0.0462 0.0487 251.555 -0.0006 -0.0085 0.0085 266.128 -0.0187 -0.0235 0.03 231.559 0.0066 -0.0057 0.0087 319.183 -3.9903

255 -0.0142 -0.0445 0.0467 252.316 -0.0018 -0.0091 0.0093 258.759 -0.0171 -0.02 0.0264 229.456 0.0046 -0.0054 0.0071 310.229 6.683

260 -0.0132 -0.043 0.045 252.944 -0.0034 -0.01 0.0105 251.223 -0.0156 -0.0165 0.0227 226.727 0.0025 -0.0051 0.0057 296.229 16.8326

265 -0.0119 -0.0416 0.0432 253.976 -0.0048 -0.0109 0.0119 246.175 -0.0142 -0.0135 0.0196 223.499 0.0008 -0.0049 0.0049 279.825 25.1679

270 -0.0115 -0.0404 0.042 254.165 -0.0072 -0.0126 0.0145 240.09 -0.0123 -0.0095 0.0156 217.819 -0.0015 -0.0046 0.0048 252.138 34.8533

275 -0.0109 -0.0387 0.0402 254.23 -0.01 -0.0144 0.0176 235.205 -0.0101 -0.0051 0.0113 206.929 -0.0037 -0.0039 0.0054 226.741 43.42

280 -0.0105 -0.0372 0.0386 254.252 -0.0129 -0.0165 0.0209 231.903 -0.0079 -0.0007 0.0079 185.127 -0.0061 -0.0034 0.007 209.325 51.0116

285 -0.01 -0.0351 0.0365 254.142 -0.016 -0.0185 0.0244 229.177 -0.0055 0.0041 0.0068 143.279 -0.0087 -0.0029 0.0091 198.323 56.8705

290 -0.0093 -0.0322 0.0335 253.797 -0.0192 -0.0204 0.028 226.647 -0.0028 0.0093 0.0097 106.726 -0.0113 -0.0021 0.0115 190.741 60.1874

295 -0.0086 -0.0281 0.0294 252.986 -0.0227 -0.0219 0.0315 223.989 0.0002 0.0152 0.0152 89.4258 -0.014 -0.0012 0.0141 184.926 59.81

300 -0.0077 -0.0223 0.0236 251.097 -0.0263 -0.0228 0.0348 220.887 0.0035 0.0219 0.0221 80.9695 -0.0169 0 0.0169 180.007 54.1236

305 -0.0064 -0.0143 0.0156 245.726 -0.0302 -0.0227 0.0378 216.992 0.0073 0.0296 0.0305 76.2092 -0.0199 0.0016 0.02 175.492 40.861

310 -0.0048 -0.0029 0.0056 211.232 -0.0343 -0.0213 0.0404 211.85 0.0117 0.0389 0.0406 73.2499 -0.0232 0.0036 0.0235 171.068 16.7632

315 -0.0024 0.0131 0.0134 100.496 -0.0388 -0.0179 0.0427 204.8 0.017 0.0503 0.0531 71.2971 -0.0268 0.0064 0.0275 166.509 -23.1012

320 0.0013 0.0372 0.0372 88.016 -0.0438 -0.0112 0.0452 194.4 0.0241 0.0657 0.0699 69.8707 -0.0309 0.0105 0.0326 161.192 -89.1936

325 0.0074 0.0718 0.0721 84.1323 -0.0488 0 0.0488 179.978 0.0328 0.0856 0.0917 69.0151 -0.0356 0.016 0.0391 155.825 -191.815

330 0.019 0.1284 0.1298 81.5973 -0.0539 0.0205 0.0577 159.141 0.0456 0.1156 0.1243 68.4796 -0.0416 0.0246 0.0484 149.383 -367.414

335 0.0567 0.28 0.2857 78.5494 -0.058 0.0806 0.0993 125.743 0.0746 0.188 0.2022 68.3448 -0.0525 0.0466 0.0702 138.385 -845.352

340 0.1688 0.647 0.6687 75.3788 -0.0438 0.242 0.2459 100.267 0.1322 0.3373 0.3623 68.6017 -0.0619 0.0965 0.1146 122.702 -2025.8

345 0.9389 2.7608 2.9161 71.2175 0.1795 1.2729 1.2855 81.9743 0.3844 1.0342 1.1034 69.6108 -0.0152 0.3616 0.3619 92.405 -8854.5

350 47.4953 104.089 114.41 65.4731 21.8217 58.8955 62.8082 69.6696 6.3215 21.2339 22.1549 73.4214 10.25 11.4584 15.374 48.1862 -337030

355 0.7576 1.1951 1.415 57.6273 0.4583 0.8456 0.9618 61.5429 -0.05 -0.0221 0.0547 203.867 0.2773 0.1022 0.2956 20.2262 -3823.9

360 0.1931 0.1882 0.2696 44.2728 0.1271 0.1853 0.2247 55.5476 -0.0403 -0.0797 0.0893 243.141 0.09 0.011 0.0907 6.9812 -572.838

Appendix A20


theta2

degree

F12x

/10.^7

N

F12y

/10.^7

N

F12

/10.^7

N

theta12

degree

F14x

/10.^7

N

F14y

/10.^7

N

F14

/10.^7

N

theta14

degree

F16x

/10.^7

N

F16y

/10.^7

N

F16

/10.^7

N

theta16

degree

0 -0.211 -0.191 0.2846 222.1524 0.1678 -0.0703 0.1819 337.2595 0.0729 -0.0926 0.1179 308.2148

5 -0.1304 -0.085 0.1557 213.0854 0.0822 -0.031 0.0879 339.3298 0.0389 -0.0556 0.0679 304.944

10 -0.1021 -0.0564 0.1166 208.9276 0.051 -0.0142 0.0529 344.4794 0.0237 -0.0387 0.0454 301.5568

15 -0.09 -0.0481 0.1021 208.1268 0.0369 -0.0055 0.0373 351.4947 0.016 -0.0291 0.0332 298.8025

20 -0.0836 -0.0445 0.0947 208.0381 0.0301 -0.0016 0.0301 356.9205 0.0115 -0.0238 0.0264 295.6907

25 -0.0793 -0.0417 0.0895 207.7227 0.0267 -0.0006 0.0267 358.7768 0.0088 -0.0209 0.0227 292.8176

30 -0.0753 -0.038 0.0844 206.7985 0.0251 -0.0013 0.0251 356.9346 0.0073 -0.0196 0.0209 290.3386

35 -0.071 -0.0334 0.0785 205.1618 0.0244 -0.0032 0.0246 352.4973 0.0065 -0.0195 0.0205 288.3428

40 -0.0659 -0.0273 0.0713 202.5227 0.0242 -0.0058 0.0249 346.6491 0.0058 -0.0203 0.0211 285.9164

45 -0.0603 -0.0211 0.0639 199.2543 0.0245 -0.0084 0.0259 341.1392 0.0057 -0.0213 0.0221 284.8557

50 -0.0543 -0.0145 0.0562 194.9753 0.025 -0.0109 0.0273 336.4252 0.0057 -0.0226 0.0233 284.135

55 -0.0479 -0.0079 0.0485 189.4147 0.0257 -0.0132 0.0289 332.7835 0.0058 -0.0239 0.0246 283.6807

60 -0.0412 -0.0016 0.0412 182.1552 0.0266 -0.0153 0.0307 330.1983 0.006 -0.0251 0.0258 283.441

65 -0.0345 0.0045 0.0348 172.6245 0.0277 -0.0169 0.0324 328.5253 0.0062 -0.0261 0.0268 283.3804

70 -0.0278 0.01 0.0295 160.2226 0.0287 -0.0182 0.034 327.5897 0.0064 -0.0269 0.0277 283.4739

75 -0.0212 0.015 0.026 144.8117 0.0298 -0.0192 0.0354 327.2314 0.0067 -0.0275 0.0283 283.7034

80 -0.0154 0.0182 0.0239 130.2089 0.0303 -0.0192 0.0359 327.6429 0.0069 -0.0277 0.0285 284.0154

85 -0.0093 0.022 0.0239 113.0455 0.0312 -0.0193 0.0367 328.1746 0.0072 -0.0278 0.0287 284.4908

90 -0.0035 0.0251 0.0254 97.9687 0.0319 -0.0192 0.0372 328.981 0.0075 -0.0277 0.0287 285.072

95 0.002 0.0278 0.0279 85.8289 0.0324 -0.0187 0.0374 329.9984 0.0077 -0.0274 0.0285 285.7514

100 0.0073 0.03 0.0308 76.3438 0.0326 -0.018 0.0373 331.1792 0.008 -0.0269 0.0281 286.5229

105 0.0122 0.0316 0.0339 68.8867 0.0326 -0.017 0.0368 332.4891 0.0082 -0.0263 0.0275 287.3809

110 0.0168 0.0328 0.0369 62.8906 0.0323 -0.0158 0.0359 333.9058 0.0084 -0.0255 0.0268 288.3198

115 0.0214 0.0337 0.0399 57.619 0.0318 -0.0147 0.035 335.1014 0.0083 -0.0241 0.0255 288.9744

120 0.0251 0.0338 0.0421 53.3963 0.0308 -0.0133 0.0335 336.6343 0.0083 -0.0229 0.0244 289.9476

125 0.0283 0.0334 0.0438 49.6746 0.0294 -0.0117 0.0316 338.2617 0.0083 -0.0216 0.0232 290.9312

130 0.0308 0.0321 0.0445 46.2638 0.0276 -0.01 0.0293 340.0232 0.0081 -0.0202 0.0218 291.8708

135 0.0321 0.0299 0.0438 42.9526 0.0254 -0.0082 0.0267 342.0087 0.0078 -0.0186 0.0202 292.6582

140 0.0317 0.026 0.041 39.3877 0.0229 -0.0064 0.0238 344.4162 0.0072 -0.0169 0.0184 293.0581

145 0.0283 0.0195 0.0344 34.5981 0.0203 -0.0044 0.0208 347.6849 0.0062 -0.0151 0.0163 292.5011

150 0.0192 0.0082 0.0209 22.9997 0.0181 -0.0023 0.0182 352.7197 0.0046 -0.0131 0.0139 289.3943

155 -0.0027 -0.0138 0.0141 258.9173 0.018 0.0001 0.018 0.3844 0.0017 -0.0114 0.0115 278.5549

160 -0.0616 -0.0647 0.0893 226.3818 0.0272 0.0032 0.0274 6.7771 -0.0044 -0.0109 0.0117 248.1332

165 -0.3605 -0.2992 0.4685 219.6905 0.1153 0.0103 0.1157 5.0889 -0.0259 -0.0251 0.0361 224.1142

170 -4.3592 -3.0589 5.3253 215.0578 1.7622 0.0077 1.7622 0.2504 -0.2191 -0.3742 0.4336 239.6455

175 -3.543 -2.0056 4.0712 209.5134 2.0748 -0.0992 2.0772 357.2631 -0.0338 -0.51 0.5111 266.204

180 -0.403 -0.1497 0.4299 200.3737 0.3653 -0.0272 0.3663 355.7442 0.0258 -0.1015 0.1047 284.2891

185 -0.1204 -0.0017 0.1204 180.8039 0.184 -0.0161 0.1847 354.9934 0.0256 -0.0552 0.0609 294.8488

190 -0.0391 0.037 0.0539 136.6168 0.1243 -0.0118 0.1248 354.5686 0.0245 -0.039 0.0461 302.0819

195 -0.0055 0.0518 0.0521 96.0953 0.0958 -0.0096 0.0962 354.2674 0.0237 -0.0307 0.0388 307.6143

200 0.0108 0.0586 0.0596 79.5519 0.0793 -0.0084 0.0797 353.9844 0.0231 -0.0255 0.0344 312.2759

205 0.0192 0.0619 0.0648 72.7769 0.0685 -0.0076 0.069 353.6706 0.0228 -0.0217 0.0315 316.4523

210 0.0234 0.0634 0.0676 69.7911 0.0609 -0.0071 0.0613 353.3051 0.0227 -0.0188 0.0294 320.331

215 0.0312 0.0666 0.0736 64.9368 0.0488 -0.0061 0.0491 352.9252 0.0212 -0.0148 0.0259 325.0517

220 0.0307 0.0663 0.073 65.1747 0.0446 -0.0059 0.045 352.4145 0.0211 -0.0129 0.0247 328.5872

225 0.0293 0.0655 0.0717 65.9033 0.0409 -0.0059 0.0414 351.8269 0.0209 -0.0111 0.0237 331.9844

230 0.0274 0.0644 0.07 66.9473 0.0376 -0.0059 0.0381 351.1366 0.0207 -0.0095 0.0228 335.2631

235 0.0253 0.0632 0.068 68.194 0.0345 -0.0059 0.035 350.3018 0.0204 -0.0081 0.0219 338.4472

240 0.023 0.0618 0.066 69.5659 0.0313 -0.0059 0.0319 349.2581 0.02 -0.0067 0.021 341.5727

245 0.0208 0.0605 0.064 71.0079 0.0281 -0.006 0.0288 347.9102 0.0194 -0.0053 0.0201 344.6947

250 0.0187 0.0592 0.062 72.4809 0.0249 -0.0062 0.0256 346.1161 0.0186 -0.004 0.019 347.8971

255 0.0167 0.0579 0.0603 73.9595 0.0216 -0.0063 0.0225 343.663 0.0175 -0.0027 0.0177 351.3079

260 0.0148 0.0568 0.0586 75.4298 0.0183 -0.0066 0.0194 340.2255 0.0162 -0.0014 0.0163 355.1285

265 0.0125 0.0555 0.0569 77.3163 0.0155 -0.0072 0.0171 335.1794 0.0151 -0.0003 0.0151 358.7222

270 0.011 0.0545 0.0556 78.6122 0.012 -0.0075 0.0141 327.9756 0.0132 0.0011 0.0132 4.6259

275 0.0094 0.0529 0.0537 79.9524 0.0084 -0.0078 0.0115 317.2548 0.0111 0.0028 0.0115 14.1236

280 0.0078 0.0512 0.0518 81.3623 0.0051 -0.0082 0.0096 302.0973 0.0086 0.0043 0.0096 26.5029

285 0.0061 0.049 0.0494 82.8761 0.0019 -0.0085 0.0087 282.8457 0.0058 0.0058 0.0082 45.2801

290 0.0044 0.0459 0.0461 84.5661 -0.0011 -0.0088 0.0089 262.7574 0.0027 0.0075 0.008 70.0877

295 0.0025 0.0415 0.0416 86.5886 -0.0041 -0.0089 0.0098 245.3959 -0.0006 0.0094 0.0094 93.6625

300 0.0004 0.0355 0.0355 89.3329 -0.0069 -0.0087 0.0111 231.4955 -0.0042 0.0114 0.0122 110.1283

305 -0.0019 0.027 0.027 94.0219 -0.0096 -0.008 0.0125 219.9401 -0.0081 0.0138 0.016 120.2728

310 -0.0046 0.0152 0.0159 106.7922 -0.0121 -0.0068 0.0139 209.3759 -0.0122 0.0166 0.0206 126.3891

315 -0.0079 -0.0012 0.008 188.9374 -0.0142 -0.0048 0.015 198.6405 -0.0167 0.0199 0.026 130.0088

320 -0.0126 -0.0256 0.0286 243.8117 -0.0157 -0.0015 0.0157 185.4687 -0.0216 0.0243 0.0325 131.6363

325 -0.0196 -0.0605 0.0636 252.0412 -0.015 0.0027 0.0152 169.8968 -0.0271 0.0296 0.0401 132.4743

330 -0.0322 -0.1172 0.1215 254.6565 -0.0098 0.0081 0.0127 140.5814 -0.0334 0.0367 0.0496 132.275

335 -0.0713 -0.2672 0.2765 255.0505 0.0181 0.0135 0.0226 36.6439 -0.0432 0.0503 0.0663 130.6552

340 -0.1863 -0.6297 0.6566 253.5179 0.1133 0.0106 0.1138 5.3618 -0.0489 0.0668 0.0828 126.1817

345 -0.9731 -2.7165 2.8855 250.2921 0.8208 -0.1083 0.8279 352.4806 0.017 0.0547 0.0573 72.7065

350 -48.4745 -103.0617 113.8925 244.8103 46.1433 -12.7337 47.868 344.5726 10.3799 -8.9013 13.6739 319.3854

355 -0.7866 -1.1898 1.4264 236.5308 0.7451 -0.2808 0.7963 339.3502 0.2536 -0.2736 0.3731 312.8191

360 -0.211 -0.191 0.2846 222.1524 0.1678 -0.0703 0.1819 337.2595 0.0729 -0.0926 0.1179 308.2148

Appendix A20


theta2

degree

F32x

/10.^7

N

F32y

/10.^7

N

F32

/10.^7

N

theta32

degree

F43x

/10.^7

N

F43y

/10.^7

N

F43

/10.^7

N

theta43

degree

F53x

/10.^7

N

F53y

/10.^7

N

F53

/10.^7

N

theta53

degree

F65x

/10.^7

N

F65y

/10.^7

N

F65

/10.^7

N

theta65

degree

T/10.^3

N.m

0 0.1974 0.1909 0.2746 44.0456 0.1309 0.1832 0.2252 54.4632 -0.0398 -0.0749 0.0848 242.039 0.0906 0.0158 0.092 9.8864 -581.113

5 0.1169 0.0838 0.1438 35.6172 0.0733 0.098 0.1224 53.1911 -0.025 -0.0562 0.0615 245.979 0.0552 0.0082 0.0558 8.4295 -222.977

10 0.0887 0.054 0.1039 31.3361 0.0515 0.0682 0.0854 52.9327 -0.0161 -0.042 0.045 248.951 0.0401 0.0073 0.0408 10.3161 -115.119

15 0.0769 0.0446 0.0889 30.0911 0.0418 0.0547 0.0688 52.5962 -0.0101 -0.0321 0.0336 252.553 0.0328 0.0081 0.0338 13.9076 -70.5117

20 0.0709 0.0398 0.0813 29.3513 0.0375 0.0468 0.0599 51.2883 -0.0065 -0.0265 0.0273 256.262 0.0289 0.0085 0.0301 16.4313 -40.2868

25 0.067 0.0359 0.076 28.1835 0.0357 0.0411 0.0545 49.0081 -0.0047 -0.0242 0.0246 259.027 0.0268 0.0084 0.0281 17.3366 -12.9247

30 0.0636 0.0312 0.0708 26.1586 0.0353 0.0365 0.0507 45.9504 -0.0044 -0.0244 0.0248 259.76 0.0258 0.0076 0.0269 16.3899 14.3551

35 0.0599 0.0255 0.0651 23.0927 0.0355 0.0324 0.0481 42.3867 -0.0054 -0.0267 0.0272 258.514 0.0254 0.0062 0.0261 13.7608 40.8092

40 0.0555 0.0186 0.0585 18.4964 0.0361 0.0287 0.0461 38.4714 -0.0078 -0.0309 0.0319 255.884 0.0249 0.004 0.0253 9.1829 65.1788

45 0.0507 0.0114 0.052 12.713 0.0369 0.0255 0.0449 34.6765 -0.0107 -0.036 0.0375 253.384 0.0249 0.0019 0.025 4.2599 84.4896

50 0.0456 0.0041 0.0457 5.1337 0.0378 0.0228 0.0442 31.0795 -0.0143 -0.0417 0.0441 251.072 0.0249 -0.0005 0.0249 358.88 98.1452

55 0.0401 -0.0032 0.0402 355.418 0.0388 0.0205 0.0439 27.8108 -0.0183 -0.0478 0.0511 249.084 0.0248 -0.0028 0.025 353.465 105.446

60 0.0344 -0.0102 0.0359 343.449 0.0398 0.0185 0.0439 24.9378 -0.0224 -0.0538 0.0583 247.425 0.0248 -0.0051 0.0253 348.349 106.246

65 0.0288 -0.0168 0.0333 329.714 0.0409 0.0169 0.0442 22.4766 -0.0265 -0.0597 0.0653 246.053 0.0246 -0.0072 0.0256 343.744 100.849

70 0.0232 -0.0228 0.0325 315.477 0.0418 0.0156 0.0446 20.4077 -0.0304 -0.065 0.0718 244.92 0.0244 -0.009 0.0261 339.749 89.8911

75 0.0177 -0.0281 0.0332 302.236 0.0426 0.0144 0.045 18.6933 -0.0341 -0.0698 0.0777 243.986 0.0242 -0.0106 0.0264 336.374 74.2217

80 0.0131 -0.0316 0.0342 292.443 0.0431 0.0137 0.0452 17.5874 -0.0364 -0.0729 0.0815 243.442 0.0239 -0.0119 0.0266 333.577 55.8612

85 0.0082 -0.0355 0.0364 282.944 0.0436 0.013 0.0455 16.584 -0.0392 -0.0763 0.0858 242.829 0.0236 -0.013 0.0269 331.192 34.154

90 0.0035 -0.0387 0.0389 275.191 0.0438 0.0124 0.0455 15.8172 -0.0414 -0.079 0.0892 242.333 0.0233 -0.0139 0.0271 329.243 10.7118

95 -0.0008 -0.0414 0.0414 268.828 0.0438 0.0119 0.0454 15.2461 -0.0432 -0.081 0.0918 241.939 0.023 -0.0145 0.0272 327.663 -13.5238

100 -0.0049 -0.0434 0.0436 263.519 0.0435 0.0115 0.045 14.8372 -0.0444 -0.0822 0.0934 241.635 0.0226 -0.015 0.0271 326.393 -37.6548

105 -0.0087 -0.0448 0.0456 258.996 0.0429 0.0111 0.0443 14.5643 -0.045 -0.0827 0.0941 241.414 0.0222 -0.0153 0.027 325.381 -60.8301

110 -0.0122 -0.0456 0.0472 255.062 0.042 0.0108 0.0434 14.4084 -0.0452 -0.0824 0.094 241.269 0.0217 -0.0154 0.0267 324.591 -82.2372

115 -0.0156 -0.046 0.0486 251.239 0.041 0.0101 0.0422 13.9056 -0.0452 -0.0812 0.0929 240.866 0.0209 -0.015 0.0257 324.215 -102.228

120 -0.0184 -0.0456 0.0492 248.086 0.0396 0.0098 0.0408 13.8466 -0.0443 -0.0793 0.0908 240.793 0.0202 -0.0147 0.025 323.885 -117.721

125 -0.0205 -0.0445 0.049 245.222 0.0379 0.0094 0.0391 13.877 -0.0428 -0.0765 0.0876 240.783 0.0195 -0.0142 0.0241 323.8 -128.874

130 -0.022 -0.0426 0.0479 242.629 0.0362 0.009 0.0373 14.0246 -0.0405 -0.0727 0.0832 240.851 0.0186 -0.0135 0.023 324.056 -134.575

135 -0.0225 -0.0395 0.0454 240.341 0.0344 0.0088 0.0355 14.3551 -0.0375 -0.0678 0.0775 241.026 0.0177 -0.0125 0.0217 324.875 -133.285

140 -0.0213 -0.0348 0.0408 238.52 0.0329 0.0088 0.034 15.002 -0.0335 -0.0613 0.0698 241.383 0.0167 -0.011 0.02 326.769 -122.584

145 -0.0172 -0.0273 0.0323 237.825 0.0321 0.0093 0.0334 16.2119 -0.0278 -0.0527 0.0596 242.132 0.0158 -0.0087 0.018 331.018 -98.1149

150 -0.0075 -0.015 0.0168 243.401 0.033 0.011 0.0348 18.3609 -0.0196 -0.0403 0.0448 244.069 0.015 -0.0051 0.0159 341.117 -50.839

155 0.015 0.008 0.017 28.158 0.0384 0.0153 0.0413 21.7506 -0.006 -0.0206 0.0215 253.796 0.0153 0.0014 0.0154 5.3586 41.4975

160 0.0744 0.06 0.0956 38.8947 0.057 0.0277 0.0634 25.906 0.0216 0.0176 0.0278 39.1726 0.0194 0.0164 0.0254 40.117 249.052

165 0.3736 0.2957 0.4764 38.3561 0.1637 0.0972 0.1904 30.7098 0.1321 0.1621 0.2091 50.8206 0.0559 0.0833 0.1003 56.1535 1163.4

170 4.3725 3.0565 5.3349 34.9544 1.6746 1.0111 1.9561 31.1227 1.3296 1.6265 2.1008 50.7368 0.7128 0.9221 1.1655 52.2949 11470

175 3.5565 2.0044 4.0824 29.4051 1.4337 0.8039 1.6437 29.2811 0.7426 0.7552 1.0591 45.4805 0.809 0.6845 1.0597 40.234 7019.4

180 0.4166 0.1496 0.4426 19.758 0.1982 0.0968 0.2206 26.0187 0.0259 -0.0207 0.0331 321.336 0.1448 0.0699 0.1608 25.7617 455.426

185 0.1339 0.0028 0.1339 1.2124 0.082 0.0327 0.0883 21.755 -0.023 -0.0639 0.0679 250.229 0.075 0.0179 0.0771 13.446 -26.8273

190 0.0525 -0.0347 0.0629 326.553 0.0467 0.0137 0.0487 16.3322 -0.0327 -0.0685 0.0759 244.471 0.0518 0.0038 0.0519 4.1845 -131.583

195 0.0186 -0.0483 0.0518 291.086 0.0309 0.0053 0.0314 9.6359 -0.0347 -0.0664 0.0749 242.405 0.0404 -0.0017 0.0404 357.565 -156.596

200 0.0019 -0.054 0.054 272.063 0.0224 0.0007 0.0224 1.7907 -0.0344 -0.0626 0.0714 241.223 0.0335 -0.0043 0.0338 352.769 -156.246

205 -0.0069 -0.0562 0.0566 263.005 0.0174 -0.002 0.0175 353.442 -0.0333 -0.0585 0.0673 240.345 0.0287 -0.0055 0.0293 349.156 -146.037

210 -0.0116 -0.0567 0.0579 258.428 0.0142 -0.0037 0.0147 345.58 -0.0319 -0.0543 0.063 239.575 0.0251 -0.0061 0.0259 346.284 -131.69

215 -0.0201 -0.0589 0.0622 251.196 0.008 -0.0073 0.0108 317.643 -0.0297 -0.0488 0.0571 238.709 0.02 -0.007 0.0212 340.647 -111.734

220 -0.0203 -0.0576 0.061 250.612 0.0068 -0.0078 0.0103 311.327 -0.0281 -0.0449 0.0529 237.948 0.0176 -0.007 0.0189 338.333 -94.5252

225 -0.0197 -0.0559 0.0593 250.599 0.006 -0.008 0.01 306.969 -0.0266 -0.0411 0.0489 237.127 0.0155 -0.0069 0.0169 336.052 -77.8881

230 -0.0187 -0.0541 0.0572 250.925 0.0053 -0.008 0.0096 303.44 -0.0251 -0.0375 0.0451 236.221 0.0135 -0.0067 0.0151 333.614 -62.097

235 -0.0175 -0.0521 0.0549 251.438 0.0045 -0.008 0.0092 299.658 -0.0236 -0.0339 0.0413 235.206 0.0116 -0.0065 0.0133 330.795 -47.2581

240 -0.0163 -0.0501 0.0527 252.032 0.0037 -0.008 0.0088 294.629 -0.0221 -0.0305 0.0377 234.048 0.0098 -0.0063 0.0116 327.299 -33.3728

245 -0.0151 -0.0482 0.0505 252.632 0.0026 -0.0082 0.0086 287.583 -0.0206 -0.0271 0.034 232.7 0.008 -0.0061 0.01 322.679 -20.3784

250 -0.014 -0.0465 0.0485 253.187 0.0013 -0.0086 0.0087 278.34 -0.0191 -0.0237 0.0304 231.089 0.0061 -0.0058 0.0084 316.215 -8.1794

255 -0.0131 -0.0449 0.0468 253.671 -0.0004 -0.0092 0.0092 267.758 -0.0175 -0.0202 0.0268 229.094 0.0042 -0.0056 0.007 306.698 3.3254

260 -0.0124 -0.0434 0.0452 254.071 -0.0023 -0.0102 0.0104 257.49 -0.0159 -0.0168 0.0231 226.496 0.0022 -0.0054 0.0058 292.302 14.2157

265 -0.0113 -0.0421 0.0436 254.942 -0.0039 -0.0111 0.0118 250.722 -0.0145 -0.0137 0.0199 223.423 0.0006 -0.0051 0.0051 276.264 23.16

270 -0.011 -0.041 0.0424 255.002 -0.0065 -0.0129 0.0145 243.206 -0.0125 -0.0098 0.0159 218.015 -0.0017 -0.0048 0.0051 250.479 33.397

275 -0.0105 -0.0394 0.0408 255.01 -0.0094 -0.0148 0.0176 237.509 -0.0103 -0.0054 0.0116 207.697 -0.0039 -0.0042 0.0057 227.186 42.4224

280 -0.0101 -0.0379 0.0392 255.031 -0.0124 -0.0169 0.021 233.776 -0.008 -0.001 0.0081 187.131 -0.0063 -0.0037 0.0073 210.728 50.4012

285 -0.0096 -0.0359 0.0372 254.995 -0.0155 -0.019 0.0246 230.85 -0.0056 0.0037 0.0067 146.23 -0.0088 -0.0032 0.0094 199.944 56.6057

290 -0.009 -0.0332 0.0344 254.823 -0.0188 -0.021 0.0282 228.267 -0.0029 0.009 0.0094 108.075 -0.0114 -0.0025 0.0117 192.346 60.2632

295 -0.0082 -0.0293 0.0304 254.346 -0.0222 -0.0227 0.0317 225.659 0 0.0148 0.0148 89.8489 -0.0142 -0.0016 0.0142 186.457 60.2635

300 -0.0072 -0.0237 0.0248 253.147 -0.0257 -0.0238 0.035 222.692 0.0034 0.0214 0.0217 81.0736 -0.017 -0.0004 0.017 181.454 55.0389

305 -0.0059 -0.0159 0.017 249.711 -0.0295 -0.0239 0.038 219.009 0.0072 0.0292 0.03 76.1981 -0.0201 0.0011 0.0201 176.858 42.3732

310 -0.0041 -0.0049 0.0064 229.656 -0.0336 -0.0228 0.0406 214.158 0.0116 0.0384 0.0401 73.1995 -0.0233 0.0031 0.0235 172.356 19.064

315 -0.0017 0.0108 0.0109 98.6942 -0.0379 -0.0197 0.0427 207.482 0.0169 0.0498 0.0526 71.2414 -0.0269 0.0059 0.0276 167.716 -19.7517

320 0.0022 0.0343 0.0344 86.2956 -0.0427 -0.0135 0.0448 197.498 0.0239 0.0651 0.0693 69.8277 -0.031 0.0099 0.0326 162.316 -84.4227

325 0.0085 0.0683 0.0688 82.8947 -0.0475 -0.0028 0.0476 183.388 0.0326 0.085 0.091 68.9994 -0.0359 0.0153 0.039 156.844 -185.1

330 0.0204 0.124 0.1256 80.6466 -0.0522 0.0168 0.0548 162.193 0.0453 0.1149 0.1235 68.5051 -0.042 0.024 0.0483 150.277 -357.811

335 0.059 0.2729 0.2792 77.7901 -0.0551 0.074 0.0922 126.649 0.074 0.1874 0.2015 68.4555 -0.0531 0.0461 0.0703 139.08 -828.526

340 0.1736 0.6343 0.6576 74.6964 -0.0377 0.229 0.2321 99.3425 0.1308 0.3376 0.3621 68.8216 -0.0633 0.0967 0.1156 123.21 -1994.4

345 0.96 2.72 2.8844 70.5603 0.206 1.2233 1.2405 80.4433 0.379 1.043 1.1097 70.0306 -0.0206 0.3703 0.3709 93.1852 -8751

350 48.4611 103.064 113.89 64.8169 22.9486 57.1514 61.5866 68.1226 6.1604 21.953 22.8009 74.3249 10.089 12.1775 15.8139 50.3585 -334470

355 0.7731 1.191 1.4199 57.011 0.4744 0.8265 0.953 60.1451 -0.0507 -0.0072 0.0512 188.062 0.2767 0.1171 0.3005 22.9451 -3815.5

360 0.1974 0.1909 0.2746 44.0456 0.1309 0.1832 0.2252 54.4632 -0.0398 -0.0749 0.0848 242.039 0.0906 0.0158 0.092 9.8864 -581.113

Appendix A21

Peak, rms value of bearing forces and driving torqure

Omega 2

rad/sSituation

Peak,

rms/mean

value

F12 (N)

/10.^7

F14 (N)

/10.^7

F16 (N)

/10.^7

F32 (N)

/10.^7

F43 (N)

/10.^7

F53 (N)

/10.^7

F65 (N)

/10.^7

T (N.m)

/10^3

peak 0.4907 0.1717 0.1250 0.4907 0.1717 0.3637 0.1250 1493.0000

rms/mean 0.0597 0.0206 0.0153 0.0597 0.0206 0.0447 0.0153 11.8571

peak 0.3211 0.4931 0.2099 0.3211 0.3049 0.1990 0.1415 805.2800

rms/mean 0.0413 0.0580 0.0249 0.0413 0.0361 0.0270 0.0171 -18.2547

peak 0.3218 0.4798 0.2144 0.3217 0.3082 0.2025 0.1433 823.6700

rms/mean 0.0413 0.0564 0.0255 0.0413 0.0364 0.0274 0.0173 18.5717

peak 0.3213 0.4931 0.2099 0.3212 0.3050 0.3050 0.1415 805.8800

rms/mean 0.0413 0.0580 0.0250 0.0413 0.0361 0.0270 0.0171 18.2620

peak 1.5103 0.6023 0.3476 1.5103 0.6023 1.0663 1.0663 45918.0000

rms/mean 0.1830 0.0717 0.0426 0.1830 0.0717 0.1310 0.1310 37.8851

peak 5.9250 3.3427 3.3427 3.4974 0.5963 0.5963 0.9538 17175.0000

rms/mean 0.6970 0.3920 0.3920 0.4100 0.0819 0.0819 0.1130 -251.6103

peak 5.9544 3.2370 1.1734 5.9541 3.5648 0.5516 0.9391 17336.0000

rms/mean 0.7000 0.3800 0.1380 0.7000 0.4180 0.0774 0.1110 -254.409411

peak 5.9252 3.3427 1.1349 5.9249 3.4975 0.5964 0.9539 17176.0000

rms/mean 0.6970 0.3920 0.1340 0.6970 0.4100 0.0819 0.1130 -251.622789

peak 3.1356 1.4633 0.6159 3.1356 1.4633 2.0611 0.6159 9506.7000

rms/mean 0.3790 0.1740 0.0764 0.3790 0.1740 0.2550 0.0764 81.5730

peak 26.8761 12.4144 3.7909 26.8752 14.9156 4.5718 3.8664 78643.0000

rms/mean 3.1500 1.4600 0.4450 3.1500 1.7500 0.5450 0.4560 -1094.8974

30

a. Only the inertial effects

are considered

b. Only the gravity forces

are neglected

c. Only the inertial effects

are neglected

d. All are considered

10


are considered


are neglected


are neglected


60


are considered


are neglected

peak 27.0032 12.0168 3.9421 27.0023 15.2100 4.4065 3.7721 79284.0000

rms/mean 3.1700 1.4100 0.4630 3.1700 1.7800 0.5260 0.4450 -1106.060382

peak 26.8763 12.4144 3.7909 26.8754 14.9157 4.5718 3.8664 78644.0000

rms/mean 3.1500 1.4600 0.4450 3.1500 1.7500 0.5450 0.4560 -1094.90949

peak 4.8833 2.5832 0.8112 4.8833 2.5832 2.9874 0.8112 14742.0000

rms/mean 0.5900 0.3070 0.1450 0.5900 0.3070 0.3700 0.1020 130.8435

peak 7.9705 62.8654 27.2557 62.8634 34.2789 11.9766 8.8201 184410.0000

rms/mean 0.9350 7.3800 3.2000 7.3700 4.0200 1.4100 1.0400 -2530.1317

peak 63.1575 63.1575 8.3080 63.1555 63.1555 11.6107 8.5841 185850.0000

rms/mean 7.4100 7.4100 0.9740 7.4100 7.4100 1.3700 1.0100 -2555.218674

peak 62.8656 27.2557 7.9705 62.8636 34.2790 34.2790 11.9766 184410.0000

rms/mean 7.3800 3.2000 0.9350 7.3700 6.9600 4.0200 1.4100 -2530.1316

peak 6.7604 3.9622 0.9436 6.7604 3.9622 3.8480 0.9436 20297.0000

rms/mean 0.8150 0.4710 0.1220 0.8150 0.4710 0.4790 0.1220 185.6822

peak 113.8923 47.868 13.6739 113.8887 61.5866 22.8009 22.8009 334470

rms/mean 1.34E+01 5.61E+00 1.60E+00 1.34E+01 7.22E+00 2.69E+00 2.69E+00 -4557.224919

peak 114.4166 46.3384 14.271 114.4132 62.8082 22.1549 15.374 337030

rms/mean 1.34E+01 5.43E+00 1.67E+00 1.34E+01 7.36E+00 2.61E+00 1.81E+00 -4601.83314

peak 113.8925 47.868 13.6739 113.8889 61.5866 22.8009 15.8139 334470

rms/mean 1.34E+01 5.61E+00 1.60E+00 1.34E+01 7.22E+00 2.69E+00 1.86E+00 -4557.229738

90


are considered


are neglected


are neglected


60c. Only the inertial effects

are neglected


120


are considered


are neglected


are neglected


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